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  • On the connectivity and restricted edge-connectivity of 3-arc graphs

     Balbuena Martinez, Maria Camino Teofila; García Vázquez, Pedro; Montejano Cantoral, Luis Pedro
    Discrete applied mathematics
    Vol. 162, p. 90-99
    DOI: 10.1016/j.dam.2013.08.010
    Date of publication: 2014-01-10
    Journal article

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    Let View the MathML source denote the symmetric digraph of a graph G. A 3-arc is a 4-tuple (y,a,b,x) of vertices such that both (y,a,b) and (a,b,x) are paths of length 2 in G. The 3-arc graphX(G) of a given graph G is defined to have vertices the arcs of View the MathML source, and they are denoted as (uv). Two vertices (ay),(bx) are adjacent in X(G) if and only if (y,a,b,x) is a 3-arc of G. The purpose of this work is to study the edge-connectivity and restricted edge-connectivity of 3-arc graphs. We prove that the 3-arc graph X(G) of every connected graph G of minimum degree d(G)=3 has ¿(X(G))=(d(G)-1)2. Furthermore, if G is a 2-connected graph, then X(G) has restricted edge-connectivity ¿(2)(X(G))=2(d(G)-1)2-2. We also provide examples showing that all these bounds are sharp. Concerning the vertex-connectivity, we prove that ¿(X(G))=min{¿(G)(d(G)-1),(d(G)-1)2}. This result improves a previous one by [M. Knor, S. Zhou, Diameter and connectivity of 3-arc graphs, Discrete Math. 310 (2010) 37¿42]. Finally, we obtain that X(G) is superconnected if G is maximally connected.

  • On the order of graphs with a given girth pair

     Balbuena Martinez, Maria Camino Teofila; Salas Piñon, Julian
    Discrete mathematics
    Vol. 321, p. 68-75
    DOI: 10.1016/j.disc.2013.12.015
    Date of publication: 2014-04-28
    Journal article

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    A (k; g, h)-graph is a k-regular graph of girth pair (g, h) where g is the girth of the graph, h is the length of a smallest cycle of different parity than g and g < h. A (k; g, h)-cage is a (k; g, h)-graph with the least possible number of vertices denoted by n(k; g, h). In this paper we give a lower bound on n(k; g, h) and as a consequence we establish that every (k; 6)-cage is bipartite if it is free of odd cycles of length at most 2k - 1. This is a contribution to the conjecture claiming that every (k; g)-cage with even girth g is bipartite. We also obtain upper bounds on the order of (k; g, h)-graphs with g = 6, 8, 12. From the proofs of these upper bounds we obtain a construction of an infinite family of small (k; g, h)-graphs. In particular, the (3; 6, h)-graphs obtained for h = 7, 9, 11 are minimal. (C) 2013 Elsevier B.V. All rights reserved.

  • Structural properties of CKI-digraphs

     Balbuena Martinez, Maria Camino Teofila; Guevara, Macuy Kak; Olsen, Mika
    AKCE International Journal of Graphs and Combinatorics
    Vol. 11, num. 1, p. 67-80
    Date of publication: 2014
    Journal article

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    A kernel of a digraph is a set of vertices which is both independent and absorbant. Let D be a digraph such that every proper induced subdigraph has a kernel. If D has a kernel, then D is kernel perfect, otherwise D is critical kernel-imperfect (for short CKI-digraph). In this work we prove that if a CKI-digraph D is not 2-arc connected, then D - a is kernel perfect for any bridge a of D. If D has no kernel but for all vertex x, D - x has a kernel, then D is called kernel critical. We give conditions on a kernel critical digraph D so that for all x 2 V (D) the kernel of D-x has at least two vertices. Concerning asymmetric digraphs, we show that every vertex u of an asymmetric CKI-digraph D on n = 5 vertices satisfies d+(u) + d-(u) = n - 3 and d+(u), d-(u) = n - 5. As a consequence, we establish that there are exactly four asymmetric CKI-digraphs on n > 7 vertices. Furthermore, we study the maximum order of a subtournament contained in a not necessarily asymmetric CKI-digraph.

  • Families of small regular graphs of girth 7

     Abreu, Marien; Araujo-Pardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Labbate, D.; Salas Piñon, Julian
    Electronic notes in discrete mathematics
    Vol. 40, p. 341-345
    DOI: 10.1016/j.endm.2013.05.060
    Date of publication: 2013-05-15
    Journal article

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    We present an explicit construction of small (q+1,7)-graphs for q a prime power that is based on some combinatorial properties of the incidence graphs of generalized quadrangles of order (q,q).

  • Bounds on the order of biregular graphs with even girth at least 8

     Lopez Chavez, G.; Araujo-Pardo, Gabriela; Montejano Peimbert, Luis; Balbuena Martinez, Maria Camino Teofila
    Electronic notes in discrete mathematics
    Vol. 40, p. 59-63
    DOI: 10.1016/j.endm.2013.05.012
    Date of publication: 2013-05-15
    Journal article

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    Let 2¿r

  • On Superconnectivity of (4, g)-Cages

     Lu, Hongliang; Wu, Yunjian; Lin, Yuqing; Yu, Qinglin; Balbuena Martinez, Maria Camino Teofila; Marcote Ordax, Francisco Javier
    Graphs and combinatorics
    Vol. 29, num. 1, p. 105-119
    DOI: 10.1007/s00373-011-1091-5
    Date of publication: 2013-01
    Journal article

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  • Large vertex-transitive graphs of diameter 2 from incidence graphs of biaffine planes

     Balbuena Martinez, Maria Camino Teofila; Miller, Mirka; Siran, Josef; Zdimalova, Maria
    Discrete mathematics
    Vol. 313, num. 19, p. 2014-2019
    DOI: 10.1016/j.disc.2013.03.007
    Date of publication: 2013-06
    Journal article

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    Under mild restrictions, we characterize all ways in which an incidence graph of a biaffine plane over a finite field can be extended to a vertex-transitive graph of diameter 2 and a given degree with a comparatively large number of vertices.

  • Biregular cages of girth five

     Abreu, Marien; Araujo-Pardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Labbate, Domenico; Lopez Chavez, G.
    Electronic journal of combinatorics
    Vol. 20, num. 1, p. 1-14
    Date of publication: 2013-03
    Journal article

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    Let 2 <= r < m and g be positive integers. An ({r, m}; g)-graph (or biregular graph) is a graph with degree set {r, m} and girth g, and an ({r, m}; g)-cage (or biregular cage) is an ({r, m}; g)-graph of minimum order n({r, m}; g). If m = r +1, an ({r,m};g)-cage is said to be a semiregular cage. In this paper we generalize the reduction and graph amalgam operations from [M. Abreu, G. Araujo Pardo, C. Balbuena, D. Labbate. Families of Small Regular Graphs of Girth 5. Discrete Math. 312(18) (2012) 2832-2842] on the incidence graphs of an affine and a biaffine plane obtaining two new infinite families of biregular cages and two new semiregular cages. The constructed new families are ({r, 2r - 3}; 5)-cages for all r = q + 1 with q a prime power, and ({r, 2r - 5}; 5)-cages for all r = q + 1 with q a prime. The new semiregular cages are constructed for r = 5 and 6 with 31 and 43 vertices respectively.

  • A note on the upper bound and girth pair of (k; g)-cages

     Balbuena Martinez, Maria Camino Teofila; González Moreno, Diego; Montellano Ballesteros, J.J.
    Discrete applied mathematics
    Vol. 161, num. 6, p. 853-857
    DOI: 10.1016/j.dam.2012.10.008
    Date of publication: 2013-04
    Journal article

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    A (k;g)(k;g)-cage is a kk-regular graph of girth gg with minimum order. In this work, for all k=3k=3 and g=5g=5 odd, we present an upper bound of the order of a (k;g+1)(k;g+1)-cage in terms of the order of a (k;g)(k;g)-cage, improving a previous result by Sauer of 1967. We also show that every (k;11)(k;11)-cage with k=6k=6 contains a cycle of length 12, supporting a conjecture by Harary and Kovács of 1983.

  • Constructions of biregular cages of girth five

     Abreu, Marien; Araujo-Pardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Labbate, D.; Lopez Chavez, G.
    Electronic notes in discrete mathematics
    Vol. 40, p. 9-14
    DOI: 10.1016/j.endm.2013.05.003
    Date of publication: 2013-05-15
    Journal article

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    Let 2¿r

  • On bi-regular cages of even girth at least 8

     Araujo-Pardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Lopez Chavez, G.; Montejano Peimbert, Luis
    Aequationes mathematicae
    Vol. 86, num. 3, p. 201-216
    DOI: 10.1007/s00010-013-0227-5
    Date of publication: 2013-12
    Journal article

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    Let r, m, 2 = r < m and g = 3 be three positive integers. A graph with a prescribed degree set r, m and girth g having the least possible number of vertices is called a bi-regular cage or an (r, m; g)-cage, and its order is denoted by n(r, m; g). In this paper we provide upper bounds on n(r, m; g) for some related values of r, m and even girth g at least 8. Moreover, if r - 1 is a prime power and m = 5, we construct the smallest currently known (r, m; 8)-graphs. Also, if r = 3 and m = 7 is not divisible by 3, we prove that n(3,m;8) = [25m/3] + 7. Finally, we construct a family of (3, m; 8)-graphs of order 9m + 3 which are cages for m = 4,5,7.

  • On the super-restricted arc-connectivity of s-geodetic digraphs

     Balbuena Martinez, Maria Camino Teofila; García Vázquez, Pedro; Hansberg Pastor, Adriana; Montejano Cantoral, Luis Pedro
    Networks
    Vol. 61, num. 1, p. 20-28
    DOI: 10.1002/net.21462
    Date of publication: 2013-01
    Journal article

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  • The k-restricted edge-connectivity of a product of graphs

     Balbuena Martinez, Maria Camino Teofila; Marcote Ordax, Francisco Javier
    Discrete applied mathematics
    Vol. 161, num. 1-2, p. 52-59
    DOI: 10.1016/j.dam.2012.08.001
    Date of publication: 2013-01
    Journal article

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    Connectivity: properties and structure  Open access

     Balbuena Martinez, Maria Camino Teofila; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel
    DOI: 10.1201/b16132
    Date of publication: 2013-12-05
    Book chapter

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    Connectivity is one of the central concepts of graph theory, from both a theoret- ical and a practical point of view. Its theoretical implications are mainly based on the existence of nice max-min characterization results, such as Menger¿s theorems. In these theorems, one condition which is clearly necessary also turns out to be sufficient. Moreover, these results are closely related to some other key theorems in graph theory: Ford and Fulkerson¿s theorem about flows and Hall¿s theorem on perfect matchings. With respect to the applications, the study of connectivity parameters of graphs and digraphs is of great interest in the design of reliable and fault-tolerant interconnection or communication networks. Since graph connectivity has been so widely studied, we limit ourselves here to the presentation of some of the key results dealing with finite simple graphs and digraphs. For results about infinite graphs and connectivity algorithms the reader can consult, for instance, Aharoni and Diestel [AhDi94], Gibbons [Gi85], Halin [Ha00], Henzinger, Rao, and Gabow [HeRaGa00], Wigderson [Wi92]. For further details, we refer the reader to some of the good textbooks and surveys available on the subject: Berge [Be76], Bermond, Homobono, and Peyrat [BeHoPe89], Frank [Fr90, Fr94, Fr95], Gross and Yellen [GrYe06], Hellwig and Volkmann [HeVo08], Lov ´asz [Lo93], Mader [Ma79], Oellermann [Oe96], Tutte [Tu66].

    Connectivity is one of the central concepts of graph theory, from both a theoret- ical and a practical point of view. Its theoretical implications are mainly based on the existence of nice max-min characterization results, such as Menger’s theorems. In these theorems, one condition which is clearly necessary also turns out to be sufficient. Moreover, these results are closely related to some other key theorems in graph theory: Ford and Fulkerson’s theorem about flows and Hall’s theorem on perfect matchings. With respect to the applications, the study of connectivity parameters of graphs and digraphs is of great interest in the design of reliable and fault-tolerant interconnection or communication networks. Since graph connectivity has been so widely studied, we limit ourselves here to the presentation of some of the key results dealing with finite simple graphs and digraphs. For results about infinite graphs and connectivity algorithms the reader can consult, for instance, Aharoni and Diestel [AhDi94], Gibbons [Gi85], Halin [Ha00], Henzinger, Rao, and Gabow [HeRaGa00], Wigderson [Wi92]. For further details, we refer the reader to some of the good textbooks and surveys available on the subject: Berge [Be76], Bermond, Homobono, and Peyrat [BeHoPe89], Frank [Fr90, Fr94, Fr95], Gross and Yellen [GrYe06], Hellwig and Volkmann [HeVo08], Lov ´asz [Lo93], Mader [Ma79], Oellermann [Oe96], Tutte [Tu66].

  • Access to the full text
    Further topics in connectivity  Open access

     Balbuena Martinez, Maria Camino Teofila; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel
    DOI: 10.1201/b16132
    Date of publication: 2013-12-05
    Book chapter

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    Continuing the study of connectivity, initiated in §4.1 of the Handbook, we survey here some (sufficient) conditions under which a graph or digraph has a given connectivity or edge-connectivity. First, we describe results concerning maximal (vertex- or edge-) connectivity. Next, we deal with conditions for having (usually lower) bounds for the connectivity parameters. Finally, some other general connectivity measures, such as one instance of the so-called ¿conditional connectivity,¿ are considered. For unexplained terminology concerning connectivity, see §4.1.

    Continuing the study of connectivity, initiated in §4.1 of the Handbook, we survey here some (sufficient) conditions under which a graph or digraph has a given connectivity or edge-connectivity. First, we describe results concerning maximal (vertex- or edge-) connectivity. Next, we deal with conditions for having (usually lower) bounds for the connectivity parameters. Finally, some other general connectivity measures, such as one instance of the so-called “conditional connectivity,” are considered. For unexplained terminology concerning connectivity, see §4.1.

  • Construction of small regular graphs of girth 7

     Salas Piñon, Julian; Balbuena Martinez, Maria Camino Teofila
    British Combinatorial Conference
    p. 1
    Presentation's date: 2013-07-02
    Presentation of work at congresses

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  • Una conjetura sobre el orden de las jaulas con pares de cinturas

     Salas Piñon, Julian; Balbuena Martinez, Maria Camino Teofila
    Encuentro Andaluz de Matemática Discreta
    p. 237-242
    Presentation's date: 2013-10-18
    Presentation of work at congresses

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    Una jaula es un grafo regular de grado k que no tiene ciclos de longitud menor que g, es decir tiene cintura g, y tiene el m´inimo n´umero de v´ertices entre todos los grafos regulares de grado k y cintura g. El n´umero de v´ertices de una jaula, se denota por n(k; g). Dados dos n´umeros g < h, el par de cinturas (g, h) en un grafo G, es tal que g es la cintura de G y h es la m´inima longitud de un ciclo de distinta paridad que g. En este trabajo presentamos resultados relacionados con la conjetura de Harary y Kov´acs que afirma que el n´umero de v´ertices de una jaula con par de cinturas (g, h) es menor que el n´umero de v´ertices de la jaula correspondiente con cintura h, i.e., n(k; g, h) = n(k; h).

  • On bi-regular cages of girth 8

     Lopez Chavez, G.; Balbuena Martinez, Maria Camino Teofila
    British Combinatorial Conference
    p. 1
    Presentation's date: 2013-07-02
    Presentation of work at congresses

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  • Families of bi-regular cages of girth 5

     Abreu, Marien; Balbuena Martinez, Maria Camino Teofila
    British Combinatorial Conference
    p. 1
    Presentation's date: 2013-07-03
    Presentation of work at congresses

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  • A sufficient condition for kernel perfectness of a digraph in terms of semikernels modulo F

     Balbuena Martinez, Maria Camino Teofila; Galeana-Sánchez, Hortensia; Guevara, Mukuy-kaak
    Acta mathematica sinica, english series
    Vol. 28, num. 2, p. 349-356
    DOI: 10.1007/s10114-012-9754-6
    Date of publication: 2012-02
    Journal article

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  • On second order degree of graphs

     Araujo-Pardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Olsen, Mika; Valencia, Pilar
    Acta mathematica sinica, english series
    Vol. 28, num. 1, p. 171-182
    DOI: 10.1007/s10114-012-9343-8
    Date of publication: 2012-01
    Journal article

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  • Girth of {C-3, ... , C-s}-free extremal graphs

     Abajo, E.; Balbuena Martinez, Maria Camino Teofila; Diánez, A.
    Discrete applied mathematics
    Vol. 160, num. 9, p. 1311-1318
    DOI: 10.1016/j.dam.2012.01.020
    Date of publication: 2012-06
    Journal article

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  • A new bound for the connectivity of cages

     Balbuena Martinez, Maria Camino Teofila; Salas Piñon, Julian
    Applied mathematics letters
    Vol. 25, num. 11, p. 1676-1680
    DOI: 10.1016/j.aml.2012.01.036
    Date of publication: 2012-11
    Journal article

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  • New results on 3-domination critical graphs

     Balbuena Martinez, Maria Camino Teofila; Hansberg Pastor, Adriana
    Aequationes mathematicae
    Vol. 83, num. 3, p. 257-269
    DOI: 10.1007/s00010-011-0105-y
    Date of publication: 2012
    Journal article

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  • Restricted arc-connectivity of generalized p-cycles

     Balbuena Martinez, Maria Camino Teofila; García Vázquez, Pedro; Hansberg Pastor, Adriana; Montejano Cantoral, Luis Pedro
    Discrete applied mathematics
    Vol. 160, num. 9, p. 1325-1332
    DOI: 10.1016/j.dam.2012.02.006
    Date of publication: 2012-06
    Journal article

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  • Families of small regular graphs of girth 5

     Abreu, Marien; Araujo-Pardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Labbate, Domenico
    Discrete mathematics
    Vol. 312, num. 18, p. 2832-2842
    DOI: 10.1016/j.disc.2012.05.020
    Date of publication: 2012-09-28
    Journal article

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  • On the Structure of Graphs without Short Cycles  Open access

     Salas Piñon, Julian
    Department of Applied Mathematics III, Universitat Politècnica de Catalunya
    Theses

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    The objective of this thesis is to study cages, constructions and properties of such families of graphs. For this, the study of graphs without short cycles plays a fundamental role in order to develop some knowledge on their structure, so we can later deal with the problems on cages. Cages were introduced by Tutte in 1947. In 1963, Erdös and Sachs proved that (k, g) -cages exist for any given values of k and g. Since then, large amount of research in cages has been devoted to their construction. In this work we study structural properties such as the connectivity, diameter, and degree regularity of graphs without short cycles. In some sense, connectivity is a measure of the reliability of a network. Two graphs with the same edge-connectivity, may be considered to have different reliabilities, as a more refined index than the edge-connectivity, edge-superconnectivity is proposed together with some other parameters called restricted connectivities. By relaxing the conditions that are imposed for the graphs to be cages, we can achieve more refined connectivity properties on these families and also we have an approach to structural properties of the family of graphs with more restrictions (i.e., the cages). Our aim, by studying such structural properties of cages is to get a deeper insight into their structure so we can attack the problem of their construction. By way of example, we studied a condition on the diameter in relation to the girth pair of a graph, and as a corollary we obtained a result guaranteeing restricted connectivity of a special family of graphs arising from geometry, such as polarity graphs. Also, we obtained a result proving the edge superconnectivity of semiregular cages. Based on these studies it was possible to develop the study of cages. Therefore obtaining a relevant result with respect to the connectivity of cages, that is, cages are k/2-connected. And also arising from the previous work on girth pairs we obtained constructions for girth pair cages that proves a bound conjectured by Harary and Kovács, relating the order of girth pair cages with the one for cages. Concerning the degree and the diameter, there is the concept of a Moore graph, it was introduced by Hoffman and Singleton after Edward F. Moore, who posed the question of describing and classifying these graphs. As well as having the maximum possible number of vertices for a given combination of degree and diameter, Moore graphs have the minimum possible number of vertices for a regular graph with given degree and girth. That is, any Moore graph is a cage. The formula for the number of vertices in a Moore graph can be generalized to allow a definition of Moore graphs with even girth (bipartite Moore graphs) as well as odd girth, and again these graphs are cages. Thus, Moore graphs give a lower bound for the order of cages, but they are known to exist only for very specific values of k, therefore it is interesting to study how far a cage is from this bound, this value is called the excess of a cage. We studied the excess of graphs and give a contribution, in the sense of the work of Biggs and Ito, relating the bipartition of girth 6 cages with their orders. Entire families of cages can be obtained from finite geometries, for example, the graphs of incidence of projective planes of order q a prime power, are (q+1, 6)-cages. Also by using other incidence structures such as the generalized quadrangles or generalized hexagons, it can be obtained families of cages of girths 8 and 12. In this thesis, we present a construction of an entire family of girth 7 cages that arises from some combinatorial properties of the incidence graphs of generalized quadrangles of order (q,q).

  • Control de invariantes en grafos sujetos a propiedades estructurales

     Marcote Ordax, Francisco Javier; Salas Piñon, Julian; Hansberg Pastor, Adriana; Cera, Martín; Gago Alvarez, Silvia; Balbuena Martinez, Maria Camino Teofila
    Competitive project

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  • Gráficas extremales con cuello al menos s

     Balbuena Martinez, Maria Camino Teofila
    Congreso Nacional de la Sociedad Matemática Mexicana
    p. 1
    Presentation's date: 2012-10-30
    Presentation of work at congresses

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  • Small girth 7 graphs from generalized quadrangles

     Salas Piñon, Julian; Abreu, Marien; Araujo-Pardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Labbate, Domenico
    Combinatorics
    p. 100
    Presentation's date: 2012-09-14
    Presentation of work at congresses

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  • Partial linear spaces and identifyng codes

     Balbuena Martinez, Maria Camino Teofila
    Encuentro Conjunto Real Sociedad Matemática Española - Sociedad Matemática Mexicana
    p. 60-61
    Presentation's date: 2012-01-18
    Presentation of work at congresses

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  • On the (lambda)'-optimality in graphs with odd girth g and even girth h

     Balbuena Martinez, Maria Camino Teofila; García-Vázquez, Pedro; Montejano Cantoral, Luis Pedro; Salas Piñon, Julian
    Applied mathematics letters
    Vol. 24, num. 7, p. 1041-1045
    DOI: 10.1016/j.aml.2011.01.015
    Date of publication: 2011-07
    Journal article

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  • Edge-superconnectivity of semiregular cages with odd girth

     Balbuena Martinez, Maria Camino Teofila; González Moreno, Diego Antonio; Salas Piñon, Julian
    networks (online)
    Vol. 58, num. 3, p. 201-206
    DOI: 10.1002/net.20431
    Date of publication: 2011-10
    Journal article

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  • Diameter and connectivity of (D; g)-cages

     Balbuena Martinez, Maria Camino Teofila; Marcote Ordax, Francisco Javier
    International journal of computer mathematics
    Vol. 88, num. 7, p. 1387-1397
    DOI: 10.1080/00207160.2010.504828
    Date of publication: 2011
    Journal article

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  • Superconnectivity of graphs with odd girth g and even girth h

     Balbuena Martinez, Maria Camino Teofila; García Vázquez, Pedro; Montejano Cantoral, Luis Pedro
    Discrete applied mathematics
    Vol. 159, num. 2-3, p. 91-99
    DOI: 10.1016/j.jfa.2010.11.013
    Date of publication: 2011-01-28
    Journal article

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  • Topological minors in bipartite graphs

     Balbuena Martinez, Maria Camino Teofila; Cera, Martín; García Vázquez, Pedro; Valenzuela, Juan Carlos
    Acta mathematica sinica, english series
    Vol. 27, num. 11, p. 2085-2100
    DOI: 10.1007/s10114-011-0149-x
    Date of publication: 2011-11
    Journal article

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  • New results on connectivity of cages

     Salas Piñon, Julian; Balbuena Martinez, Maria Camino Teofila
    Electronic notes in discrete mathematics
    Vol. 38, p. 93-99
    DOI: 10.1016/j.endm.2011.09.016
    Date of publication: 2011-12-01
    Journal article

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  • Partial linear spaces and identifying codes

     Araujo-Pardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Valenzuela, Juan Carlos; Montejano Cantoral, Luis Pedro
    European journal of combinatorics
    Vol. 32, num. 3, p. 344-351
    DOI: 10.1016/j.ejc.2010.10.014
    Date of publication: 2011-04
    Journal article

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  • A sufficient degree condition for a graph to contain all trees of size k

     Balbuena Martinez, Maria Camino Teofila; Márquez, Alberto; Portillo, Jose Ramón
    Acta mathematica sinica, english series
    Vol. 27, num. 1, p. 135-140
    DOI: 10.1007/s10114-011-9617-6
    Date of publication: 2011-01
    Journal article

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  • Monotonicity of the order of (D, g)-cages

     Balbuena Martinez, Maria Camino Teofila; Marcote Ordax, Francisco Javier
    Applied mathematics letters
    Vol. 24, num. 11, p. 1933-1937
    DOI: 10.1016/j.aml.2011.05.024
    Date of publication: 2011-11
    Journal article

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  • Constructions of small regular bipartite graphs of girth 6

     Araujo-Pardo, Gabriela; Balbuena Martinez, Maria Camino Teofila
    networks (online)
    Vol. 57, num. 2, p. 121-127
    DOI: 10.1002/net.20392
    Date of publication: 2011-03
    Journal article

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    In this article, some structures in the projective plane of order q are found which allow us to construct small k - regular balanced bipartite graphs of girth 6 for all k ≤ q. When k = q, the order of these q-regular graphs is 2(q^2−1); and when k ≤ q−1, the order of these k -regular graphs is 2(qk − 2). Moreover, the incidence matrix of a k -regular balanced bipartite graph of girth 6 having 2(qk −2) vertices, where k is an integer and q is a prime power with 3 ≤ k ≤ q − 1, is provided. These graphs improve upon the best known upper bounds for the number of vertices in regular graphs of girth 6.

  • Regular partial linear spaces admitting identifying codes

     Balbuena Martinez, Maria Camino Teofila; Araujo-Pardo, Gabriela; Montejano Cantoral, Luis Pedro; Valenzuela, Juan Carlos
    Bordeaux Workshop on Identifying Codes
    p. 5
    Presentation's date: 2011-11-21
    Presentation of work at congresses

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  • Minimally restricted 2-edge connected graphs

     Valenzuela, Juan Carlos; Balbuena Martinez, Maria Camino Teofila; Cera, Martín; García-Vázquez, Pedro
    Slovenian International Conference on Graph Theory
    p. 163-
    Presentation's date: 2011-06-24
    Presentation of work at congresses

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  • On the optimal restricted arc-connectivity of digraphs

     García-Vázquez, Pedro; Balbuena Martinez, Maria Camino Teofila; Hansberg, Adriana; Montejano Cantoral, Luis Pedro
    Slovenian International Conference on Graph Theory
    p. 150
    Presentation's date: 2011-06-23
    Presentation of work at congresses

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  • RESTRICTED CONNECTIVITY IN FAMILIES OF GRAPHS

     Montejano Cantoral, Luis Pedro
    Department of Applied Mathematics III, Universitat Politècnica de Catalunya
    Theses

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  • An explicit formula for obtaining generalized quadrangles and other small regular graphs of girth 8

     Balbuena Martinez, Maria Camino Teofila; Araujo-Pardo, Gabriela; Abreu, Marien; Labbate, Domenico
    International Workshop on Optimal Network Topologies
    Presentation's date: 2011-07-11
    Presentation of work at congresses

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  • An explicit formula for obtaining generalized quadrangles and other small regular graphs of girth 8

     Balbuena Martinez, Maria Camino Teofila; Araujo-Pardo, Gabriela; Abreu, Marien; Labbate, Domenico
    Slovenian International Conference on Graph Theory
    p. 130
    Presentation's date: 2011-06-24
    Presentation of work at congresses

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  • Results on 3-domination critical graphs

     Balbuena Martinez, Maria Camino Teofila; Hansberg Pastor, Adriana
    Colourings, Independence and Domination: Workshop on Graph Theory
    Presentation's date: 2011-09-18
    Presentation of work at congresses

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  • Access to the full text
    Una fórmula explícita para obtener cuadrángulos generalizados y otros grafos pequeños de cintura 8  Open access

     Abreu, Marien; Balbuena Martinez, Maria Camino Teofila; Araujo-Pardo, Gabriela; Labbate, Domenico
    Encuentro Andaluz de Matemática Discreta
    p. 137-143
    Presentation's date: 2011-11-08
    Presentation of work at congresses

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    Para cada potencia de primo q, se han constru do (q+1; 8)-jaulas como super cies cu adricas no degeneradas en 4-espacios proyectivos P(4; q). En primer lugar presentamos una construcci on de estos grafos de un modo alternativo dando una f ormula expl cita en la que usamos terminolog a gr a ca. Adem as derivamos grafos k-regulares de cintura 8 para grados k = q; q 1 que tienen el n umero m as peque~no de v ertices conocido hasta ahora.

  • Sobre la conectividad del grafo producto G * H

     Balbuena Martinez, Maria Camino Teofila; Marcote Ordax, Francisco Javier
    Encuentro Andaluz de Matemática Discreta
    p. 33-37
    Presentation's date: 2011-11-07
    Presentation of work at congresses

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