 Research group
 COMBGRAF  Combinatorics, Graph Theory and Applications
 Department
 Department of Applied Mathematics III
 School
 Barcelona School of Civil Engineering (ETSECCPB)
 m.camino.balbuenaupc.edu
 Contact details
 UPC directory
 Orcid
 http://orcid.org/0000000341904287
 ResearcherID
 A10622010
 Scopus Author ID
 35617500700
Scientific and technological production


On the connectivity and restricted edgeconnectivity of 3arc graphs
Balbuena Martinez, Maria Camino Teofila; García Vázquez, Pedro; Montejano Cantoral, Luis Pedro
Discrete applied mathematics
Date of publication: 20140110
Journal article
Read the abstract View Share Reference managersLet View the MathML source denote the symmetric digraph of a graph G. A 3arc is a 4tuple (y,a,b,x) of vertices such that both (y,a,b) and (a,b,x) are paths of length 2 in G. The 3arc 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 3arc of G. The purpose of this work is to study the edgeconnectivity and restricted edgeconnectivity of 3arc graphs. We prove that the 3arc 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 2connected graph, then X(G) has restricted edgeconnectivity ¿(2)(X(G))=2(d(G)1)22. We also provide examples showing that all these bounds are sharp. Concerning the vertexconnectivity, 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 3arc 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
Date of publication: 20140428
Journal article
Read the abstract View Share Reference managersA (k; g, h)graph is a kregular 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. 
Large vertextransitive graphs of diameter 2 from incidence graphs of biaffine planes
Balbuena Martinez, Maria Camino Teofila; Miller, Mirka; Siran, Josef; Zdimalova, Maria
Discrete mathematics
Date of publication: 201306
Journal article
Read the abstract View Share Reference managersUnder mild restrictions, we characterize all ways in which an incidence graph of a biaffine plane over a finite field can be extended to a vertextransitive graph of diameter 2 and a given degree with a comparatively large number of vertices. 
Biregular cages of girth five
Abreu, Marien; AraujoPardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Labbate, Domenico; Lopez Chavez, G.
Electronic journal of combinatorics
Date of publication: 201303
Journal article
Read the abstract View Share Reference managersLet 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) 28322842] 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
Date of publication: 201304
Journal article
Read the abstract View Share Reference managersA (k;g)(k;g)cage is a kkregular 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. 
Connectivity: properties and structure
Balbuena Martinez, Maria Camino Teofila; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel
Date of publication: 20131205
Book chapter
Read the abstract View Share Reference managersConnectivity 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 maxmin 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 faulttolerant 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]. 
Further topics in connectivity
Balbuena Martinez, Maria Camino Teofila; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel
Date of publication: 20131205
Book chapter
Read the abstract View Share Reference managersContinuing 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 edgeconnectivity. 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 socalled ¿conditional connectivity,¿ are considered. For unexplained terminology concerning connectivity, see §4.1. 
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
Presentation's date: 20131018
Presentation of work at congresses
Read the abstract View Share Reference managersUna 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 the superrestricted arcconnectivity of sgeodetic digraphs
Balbuena Martinez, Maria Camino Teofila; García Vázquez, Pedro; Hansberg Pastor, Adriana; Montejano Cantoral, Luis Pedro
networks
Date of publication: 201301
Journal article
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The krestricted edgeconnectivity of a product of graphs
Balbuena Martinez, Maria Camino Teofila; Marcote Ordax, Francisco Javier
Discrete applied mathematics
Date of publication: 201301
Journal article
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On biregular cages of even girth at least 8
AraujoPardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Lopez Chavez, G.; Montejano Peimbert, Luis
Aequationes mathematicae
Date of publication: 201312
Journal article
Read the abstract View Share Reference managersLet 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 biregular 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. 
Families of small regular graphs of girth 7
Abreu, Marien; AraujoPardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Labbate, D.; Salas Piñon, Julian
Electronic notes in discrete mathematics
Date of publication: 20130515
Journal article
Read the abstract View Share Reference managersWe 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.; AraujoPardo, Gabriela; Montejano Peimbert, Luis; Balbuena Martinez, Maria Camino Teofila
Electronic notes in discrete mathematics
Date of publication: 20130515
Journal article
Read the abstract View Share Reference managersLet 2¿r 
Constructions of biregular cages of girth five
Abreu, Marien; AraujoPardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Labbate, D.; Lopez Chavez, G.
Electronic notes in discrete mathematics
Date of publication: 20130515
Journal article
Read the abstract View Share Reference managersLet 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
Date of publication: 201301
Journal article
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Girth of {C3, ... , Cs}free extremal graphs
Abajo, E.; Balbuena Martinez, Maria Camino Teofila; Diánez, A.
Discrete applied mathematics
Date of publication: 201206
Journal article
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Families of small regular graphs of girth 5
Abreu, Marien; AraujoPardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Labbate, Domenico
Discrete mathematics
Date of publication: 20120928
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
Date of publication: 201211
Journal article
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On the Structure of Graphs without Short Cycles
Salas Piñon, Julian
Defense's date: 20121220
Department of Applied Mathematics III, Universitat Politècnica de Catalunya
Theses
Read the abstract Access to the full text Share Reference managersThe 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 edgeconnectivity, may be considered to have different reliabilities, as a more refined index than the edgeconnectivity, edgesuperconnectivity 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/2connected. 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
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New results on 3domination critical graphs
Balbuena Martinez, Maria Camino Teofila; Hansberg Pastor, Adriana
Aequationes mathematicae
Date of publication: 2012
Journal article
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Restricted arcconnectivity of generalized pcycles
Balbuena Martinez, Maria Camino Teofila; García Vázquez, Pedro; Hansberg Pastor, Adriana; Montejano Cantoral, Luis Pedro
Discrete applied mathematics
Date of publication: 201206
Journal article
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A sufficient condition for kernel perfectness of a digraph in terms of semikernels modulo F
Balbuena Martinez, Maria Camino Teofila; GaleanaSánchez, Hortensia; Guevara, Mukuykaak
Acta mathematica sinica, english series
Date of publication: 201202
Journal article
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On second order degree of graphs
AraujoPardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Olsen, Mika; Valencia, Pilar
Acta mathematica sinica, english series
Date of publication: 201201
Journal article
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An explicit formula for obtaining generalized quadrangles and other small regular graphs of girth 8
Balbuena Martinez, Maria Camino Teofila; AraujoPardo, Gabriela; Abreu, Marien; Labbate, Domenico
International Workshop on Optimal Network Topologies
Presentation's date: 20110711
Presentation of work at congresses
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Sobre la conectividad del grafo producto G * H
Balbuena Martinez, Maria Camino Teofila; Marcote Ordax, Francisco Javier
Encuentro Andaluz de Matemática Discreta
Presentation's date: 20111107
Presentation of work at congresses
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Una fórmula explícita para obtener cuadrángulos generalizados y otros grafos pequeños de cintura 8
Abreu, Marien; Balbuena Martinez, Maria Camino Teofila; AraujoPardo, Gabriela; Labbate, Domenico
Encuentro Andaluz de Matemática Discreta
Presentation's date: 20111108
Presentation of work at congresses
Read the abstract Access to the full text Share Reference managersPara cada potencia de primo q, se han constru do (q+1; 8)jaulas como super cies cu adricas no degeneradas en 4espacios 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 kregulares de cintura 8 para grados k = q; q 1 que tienen el n umero m as peque~no de v ertices conocido hasta ahora. 
Constructions of small regular bipartite graphs of girth 6
AraujoPardo, Gabriela; Balbuena Martinez, Maria Camino Teofila
networks
Date of publication: 201103
Journal article
Read the abstract View Share Reference managersIn 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 qregular 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. 
Partial linear spaces and identifying codes
AraujoPardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Valenzuela, Juan Carlos; Montejano Cantoral, Luis Pedro
European journal of combinatorics
Date of publication: 201104
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
Date of publication: 20110128
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
Date of publication: 201111
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
Date of publication: 20111201
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
Date of publication: 201111
Journal article
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RESTRICTED CONNECTIVITY IN FAMILIES OF GRAPHS
Montejano Cantoral, Luis Pedro
Defense's date: 20110915
Department of Applied Mathematics III, Universitat Politècnica de Catalunya
Theses
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Edgesuperconnectivity of semiregular cages with odd girth
Balbuena Martinez, Maria Camino Teofila; González Moreno, Diego Antonio; Salas Piñon, Julian
networks
Date of publication: 201110
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
Date of publication: 2011
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
Date of publication: 201101
Journal article
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On the (lambda)'optimality in graphs with odd girth g and even girth h
Balbuena Martinez, Maria Camino Teofila; GarcíaVázquez, Pedro; Montejano Cantoral, Luis Pedro; Salas Piñon, Julian
Applied mathematics letters
Date of publication: 201107
Journal article
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On the restricted edgeconnectivity of 3arc graphs
Balbuena Martinez, Maria Camino Teofila; GarcíaVázquez, Pedro; Montejano Cantoral, Luis Pedro
Jornadas de Matemática Discreta y Algorítmica
Presentation's date: 201007
Presentation of work at congresses
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Regular parcial linear spaces admitting (1; = k)identifying codes
AraujoPardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Valenzuela, Juan Carlos; Montejano Cantoral, Luis Pedro
Jornadas de Matemática Discreta y Algorítmica
Presentation's date: 201007
Presentation of work at congresses
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Edge fault tolerance analysis of super krestricted connected networks
Balbuena Martinez, Maria Camino Teofila; García Vázquez, Pedro
Applied mathematics and computation
Date of publication: 20100315
Journal article
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Adjacency matrices of polarity graphs and of other C4free graphs of large size
Abreu, Marien; Balbuena Martinez, Maria Camino Teofila; Labbate, Domenico
Designs codes and cryptography
Date of publication: 2010
Journal article
Read the abstract View Share Reference managersIn this paper we give a method for obtaining the adjacency matrix of a simple polarity graph $G_q$ from a projective plane PG(2,q), where q is a prime power. Denote by ex(n;C₄) the maximum number of edges of a graph on n vertices and free of squares C₄. We use the constructed graphs $G_q$ to obtain lower bounds on the extremal function ex(n;C₄), for some n < q² + q + 1. In particular, we construct a C₄free graph on n = q² − √q vertices and 1/2q(q²−1) − 1/2√q(q − 1) edges, for a square prime power q. 
New families of graphs without short cycles and large size
Abajo, E.; Balbuena Martinez, Maria Camino Teofila; Diánez, A.
Discrete applied mathematics
Date of publication: 20100606
Journal article
Read the abstract View Share Reference managersWe denote by ex $(n; {C^3,C^4,…Cs})$ or fs(n) the maximum number of edges in a graph of order n and girth at least s+1. First we give a method to transform an nvertex graph of girth g into a graph of girth at least g1 on fewer vertices. For an infinite sequence of values of n and s∈{4, 6, 10} the obtained graphs are denser than the known constructions of graphs of the same girth s+1. We also give another different construction of dense graphs for an infinite sequence of values of n and s∈{7, 11}. These two methods improve the known lower bounds on fs(n) for s ∊ {4, 6, 7, 10, 11} which were obtained using different algorithms. Finally, to know how good are our results, we have proved that $\limsup_{n\longrightarrow{\infty}}\displaystyle\frac{\int_s (n)}{n^{1+\displaystyle\frac{2}{s1}}}=2^{1\displaystyle\frac{2}{s1}}$ for s ∊ 2 {5, 7, 11}, and $s^{1\displaystyle\frac{2}{s}}$ ≤ $\limsup_{n\longrightarrow{\infty}}\displaystyle\frac{\int_s (n)}{n^{1+\displaystyle\frac{2}{s}}}$ ≤ 0.5 for s ∊ {6, 10}. 
On the connectivity and superconnected graphs with small diameter
Balbuena Martinez, Maria Camino Teofila; Marshall, Kim; Montejano Cantoral, Luis Pedro
Discrete applied mathematics
Date of publication: 20100306
Journal article
Read the abstract View Share Reference managersIn this paper, first we prove that any graph G is 2connected if diam (G)≤ g1 for even girth g, and for odd girth g and maximum degree $\Delta$ ≤ 2$\delta$1 where $\delta$ is the minimum degree. Moreover, we prove that any graph G of diameter diam(G) ≤ g2 satisfies that (i)G is 5connected for even girth g and $\Delta$ ≤ 2$\delta$5, and (ii)G is superk for odd girth g and $\Delta$ ≤ 3$\delta$/21. 
Finding small regular graphs of girths 6, 8 and 12 as subgraphs of cages
AraujoPardo, Gabriela; Balbuena Martinez, Maria Camino Teofila; Héger, T.
Discrete mathematics
Date of publication: 201004
Journal article
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On the restricted edgeconnectivity of 3arc graphs
Balbuena Martinez, Maria Camino Teofila; GarcíaVázquez, Pedro; Montejano Cantoral, Luis Pedro
Date of publication: 20100609
Book chapter
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On identifying codes in partial linear spaces
Balbuena Martinez, Maria Camino Teofila
Date of publication: 20100609
Book chapter
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Subdivisions in a bipartite graph
Balbuena Martinez, Maria Camino Teofila; Cera, Martín; GarcíaVázquez, Pedro; Valenzuela, Juan Carlos
Date of publication: 20100609
Book chapter
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On the krestricted edgeconnectivity of matched sum graphs
Balbuena Martinez, Maria Camino Teofila; Marcote Ordax, Francisco Javier
Date of publication: 20100609
Book chapter
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INTERNATIONAL WORKSHOP ON OPTIMAL NETWORK TOPOLOGIES
Balbuena Martinez, Maria Camino Teofila; Mitjana Riera, Margarida; Serra Albo, Oriol; Fàbrega Canudas, Josep; Comellas Padro, Francesc de Paula
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