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1 to 31 of 31 results
  • On vosperian and superconnected vertex-transitive digraphs

     Hamidoune, Yahya O.; Llado Sanchez, Anna; López Masip, Susana Clara
    Graphs and combinatorics
    Date of publication: 2013
    Journal article

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  • Small cutsets in arc-transitive digraphs of prime degree

     López Masip, Susana Clara
    Discrete applied mathematics
    Date of publication: 2013-03-05
    Journal article

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    We give an upper bound for the size of non-trivial sets that have small boundary in a family of arc-transitive digraphs. We state the exact size for these sets in case of prime degree. We also give a lower bound for the size of a minimum non-trivial cutset in the case of arc-transitive Cayley digraphs of prime degree.

  • New problems related to the valences of (super) edge-magic labeling

     López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
    AKCE International Journal of Graphs and Combinatorics
    Date of publication: 2013-08
    Journal article

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    A graph G of order p and size q is edge-magic if there is a bijective function f : V(G) ¿ E(G) ¿ {i}p+q i=1 such that f(x) + f(xy) + f(y) = k, for all xy ¿ E(G). The function f is an edge-magic labeling of G and the sum k is called either the magic sum, the valence or theweight of f. Furthermore, if f(V(G)) = {i}p i=1 then f is a super edge-magic labeling of G. In this paper we study the valences that can be attained by (super) edge-magic labelings of some families of graphs

  • Labeling constructions using digraphs products

     López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
    Discrete applied mathematics
    Date of publication: 2013-12
    Journal article

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    In this paper we study the edge-magicness of graphs with equal size and order, and we use such graphs and digraph products in order to construct labelings of different classes and of different graphs. We also study super edge-magic labelings of 22-regular graphs with exactly two components and their implications to other labelings. The strength of the paper lays on the techniques used, since they are not only used in order to provide labelings of many different types of families of graphs, but they also show interesting relations among well studied types of labelings. We are able to obtain, in this way, deep results relating different types of labelings.

  • The jumping knight and other (super) edge-magic constructions

     López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
    Mediterranean journal of mathematics
    Date of publication: 2013-11
    Journal article

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    Let G be a graph of order p and size q with loops allowed. A bijective function f:V(G)¿E(G)¿{i}p+qi=1 is an edge-magic labeling of G if the sum f(u)+f(uv)+f(v)=k is independent of the choice of the edge uv. The constant k is called either the valence, the magic weight or the magic sum of the labeling f. If a graph admits an edge-magic labeling, then it is called an edge-magic graph. Furthermore, if the function f meets the extra condition that f(V(G))={i}pi=1 then f is called a super edge-magic labeling and G is called a super edge-magic graph. A digraph D admits a labeling, namely l, if its underlying graph, und(D) admits l. In this paper, we introduce a new construction of super edge-magic labelings which are related to the classical jump of the knight on the chess game. We also use super edge-magic labelings of digraphs together with a generalization of the Kronecker product to get edge-magic labelings of some families of graphs.

  • New problems related to the number of valences of (S)EM labelings

     López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
    AKCE International Journal of Graphs and Combinatorics
    Date of publication: 2013-08
    Journal article

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    A graph G of order p and size q is edge-magic if there is a bijective function f : V (G) [E(G) -! {i}p+q i=1 such that f(x) + f(xy) + f(y) = k, for all xy 2 E(G). The function f is an edge-magic labeling of G and the sum k is called either the magic sum, the valence or the weight of f. Furthermore, if f(V (G)) = {i}p i=1 then f is a super edge-magic labeling of G. In this paper we study the valences that can be attained by (super) edge-magic labelings of some families of graphs.

  • Large restricted sumsets in general Abelian groups

     Hamidoune, Yayha Old; López Masip, Susana Clara; Plagne, Alain
    European journal of combinatorics
    Date of publication: 2013-11
    Journal article

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    Let A, B and S be subsets of a finite Abelian group G. The restricted sumset of A and B with respect to S is defined as A¿SB = {a + b : a ¿ A, b ¿ Banda - b ¿ S} Let L S = max z ¿G| { (x, y) : x, y ¿ G, x + y = zandx - y ¿ S} |. A simple application of the pigeonhole principle shows that |A| + |B| > |G| + L S implies A¿SB = G. We then prove that if |A| + |B| = |G| + L S then |A¿SB| = |G| - 2|S|. We also characterize the triples of sets (A, B, S) such that |A| + |B| = |G| + L S and |A¿SB| = |G| - 2|S|. Moreover, in this case, we also provide the structure of the set G {set minus} (A¿SB) .

  • Perfect super edge-magic graphs

     López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
    BULL. MATH. SOC.SCI. MATH. ROUMANIE,
    Date of publication: 2012-05-11
    Journal article

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  • On super edge-magic decomposable graphs

     López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
    Indian journal of pure and applied mathematics
    Date of publication: 2012-10-01
    Journal article

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  • Open problems involving super edge-magic labelings and other related topics

     López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
    Bulletin of the Institute of Combinatorics and its Applications
    Date of publication: 2012
    Journal article

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    Graph labelings has experimented a fast development during the last four decades. Two books dedicated to this topic, a very complete survey on the subject and over 1000 papers in the literature constitute a good proof of this fact. In this paper we explore some open problems on super edge-magic labelings, and about related topics. We are particularly interested on super edge-magic labelings due to the large amount of relations existing among super edge-magic labelings and other types of labelings, mainly graceful and harmonious labelings.

  • Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación

     Aguilo Gost, Francisco de Asis Luis; Abiad Monge, Aida; Andrés Yebra, José Luis; Barriere Figueroa, Eulalia; Cámara Vallejo, Marc; Ball, Simeon Michael; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Fàbrega Canudas, Josep; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Pérez Mansilla, Sonia; Rius Font, Miquel; Serra Albo, Oriol; Vena, Lluis; Vilaltella Castanyer, Joan; Zaragoza Monroig, Maria Luisa; Espona Dones, Margarida; Sau Valls, Ignasi; Montejano Cantoral, Amanda; Perarnau Llobet, Guillem; Moragas Vilarnau, Jordi; Vena Cros, Lluís; Andres Yebra, Jose Luis; Fiol Mora, Miquel Àngel
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  • The power of digraph products applied to labelings

     Ichishima, Rikio; López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
    Discrete mathematics
    Date of publication: 2011-09-23
    Journal article

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  • Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors

     Hamidoune, Yayha Old; Llado Sanchez, Anna; López Masip, Susana Clara
    Journal of graph theory
    Date of publication: 2011-06
    Journal article

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    A d-regular graph is said to be superconnected if any disconnecting subset with cardinality at most d is formed by the neighbors of some vertex. A superconnected graph that remains connected after the failure of a vertex and its neighbors will be called vosperian. Let Γ be a vertex-transitive graph of degree d with order at least d+4. We give necessary and sufficient conditions for the vosperianity of Γ. Moreover, assuming that distinct vertices have distinct neighbors, we show that Γ is vosperian if and only if it is superconnected. Let G be a group and let S⊂G\{1} with S=S−1. We show that the Cayley graph, Cay(G, S), defined on G by S is vosperian if and only if G\(S∪{1}) is not a progression and for every non-trivial subgroup H and every a∈G, If moreover S is aperiodic, then Cay(G, S) is vosperian if and only if it is superconnected.

  • Vertex-transitive graphs that remain connected after failure of a vertex and its neighbors

     Hamidoune, Yayha Old; Llado Sanchez, Anna; López Masip, Susana Clara
    Journal of graph theory
    Date of publication: 2011-12-05
    Journal article

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  • Bi-magic and other generalizations of super edge-magic labelings

     López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
    Bulletin of the Australian Mathematical Society
    Date of publication: 2011-06-15
    Journal article

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    In this paper, we use the product ⊗h in order to study super edge-magic labelings, bi-magic labelings and optimal k-equitable labelings. We establish, with the help of the product ⊗h, new relations between super edge-magic labelings and optimal k-equitable labelings and between super edge-magic labelings and edge bi-magic labelings. We also introduce new families of graphs that are inspired by the family of generalized Petersen graphs. The concepts of super bi-magic and r-magic labelings are also introduced and discussed, and open problems are proposed for future research.

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    Enumerating super edge-magic labelings for the union of non-isomorphic graphs  Open access

     Ahmad, Ali; López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
    Bulletin of the Australian Mathematical Society
    Date of publication: 2011-10-15
    Journal article

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    A super edge-magic labeling of a graph G=(V,E) of order p and size q is a bijection f:V ∪E→{i}p+qi=1 such that: (1) f(u)+f(uv)+f(v)=k for all uv∈E; and (2) f(V )={i}pi=1. Furthermore, when G is a linear forest, the super edge-magic labeling of G is called strong if it has the extra property that if uv∈E(G) , u′,v′ ∈V (G) and dG (u,u′ )=dG (v,v′ )<+∞, then f(u)+f(v)=f(u′ )+f(v′ ). In this paper we introduce the concept of strong super edge-magic labeling of a graph G with respect to a linear forest F, and we study the super edge-magicness of an odd union of nonnecessarily isomorphic acyclic graphs. Furthermore, we find exponential lower bounds for the number of super edge-magic labelings of these unions. The case when G is not acyclic will be also considered.

  • Super edge-magic models

     López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
    Mathematics in computer science
    Date of publication: 2011-04-20
    Journal article

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    Problemas abiertos sobre etiquetamientos super edge-magic y temas relacionados  Open access

     López Masip, Susana Clara; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
    Jornadas de Matemática Discreta y Algorítmica
    Presentation's date: 2010-07-07
    Presentation of work at congresses

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    El tema de los etiquetamientos de grafos ha experimentado un fuerte impulso en los últimos 40 años, muestra de ello son los dos libros dedicados en exclusiva a ellos, un completísimo artículo ”survey” y más de 1000 artículos en la literatura. En este artículo exploramos algunas preguntas abiertas sobre etiquetamientos super edge-magic. Nos interesa particularmente este tipo de etiquetamientos, debido a la cantidad de relaciones que poseen con otras clases de etiquetamientos, principalmente los graciosos y los armónicos.

  • Every tree is a large subtree of a tree that decomposes Kn or Kn,n

     Llado Sanchez, Anna; López Masip, Susana Clara; Moragas Vilarnau, Jordi
    Discrete mathematics
    Date of publication: 2010-02-28
    Journal article

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    Let T be a tree with m edges. A well-known conjecture of Ringel states that T decomposes the complete graph $K_{2m+1}$. Graham and Häggkvist conjectured that T also decomposes the complete bipartite graph $K_{m,m}$. In this paper we show that there exists an integer n with n ≤[(3m - 1)/2] and a tree T₁ with n edges such that T₁ decomposes $K_{2n+1}$ and contains T. We also show that there exists an integer n' with n' ≥ 2m-1 and a tree T₂ with n' edges such that T₂ decomposes $K_{n',n'}$and contains T. In the latter case, we can improve the bound if there exists a prime p such that [3m/2] ≤ p < 2m - 1.

  • PROBLEMAS EXTREMALES Y DE OPTIMIZACIÓN EN TEORIA DE GRAFOS Y COMBINATORIA: APLICACIÓN AL ANALISIS Y ALGORITMOS DE REDES DE COMUNICAC

     Abiad Monge, Aida; Andres Yebra, Jose Luis; Aguilo Gost, Francisco de Asis Luis; Aroca Farrerons, Josep Maria; Ball, Simeon Michael; Barajas Tomas, Javier; Barguilla Navarrete, Jorge; Barriere Figueroa, Eulalia; Cámara Vallejo, Marc; Comellas Padro, Francesc de Paula; Dalfo Simo, Cristina; Espona Dones, Margarida; Fàbrega Canudas, Josep; Gago Alvarez, Silvia; Garriga Valle, Ernest; Gomez Marti, Jose; Llado Sanchez, Anna; López Masip, Susana Clara; Miralles De La Asuncion, Alicia; Mitjana Riera, Margarida; Montejano Cantoral, Amanda; Moragas Vilarnau, Jordi; Muñoz Lopez, Francisco Javier; Pelayo Melero, Ignacio Manuel; Perarnau Llobet, Guillem; Pérez Mansilla, Sonia; Rius Font, Miquel; Sau Valls, Ignasi; Serra Albo, Oriol; Vena, Lluis; Vilaltella Castanyer, Joan; Zaragoza Monroig, Maria Luisa; Vena Cros, Lluís; Fiol Mora, Miquel Àngel
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  • COMBINATÒRIA , TEORIA DE GRAFS I APLICACIONS

     Moragas Vilarnau, Jordi; Comellas Padro, Francesc de Paula; López Masip, Susana Clara; Mitjana Riera, Margarida; Llado Sanchez, Anna; Barriere Figueroa, Eulalia; Gomez Marti, Jose; Miralles De La Asuncion, Alicia; Pérez Mansilla, Sonia; Muñoz Lopez, Francisco Javier; Zaragoza Monroig, Maria Luisa; Dalfo Simo, Cristina; Garriga Valle, Ernest; Espona Dones, Margarida; Rius Font, Miquel; Aguilo Gost, Francisco de Asis Luis; Aroca Farrerons, Josep Maria; Cámara Vallejo, Marc; Gago Alvarez, Silvia; Ball, Simeon Michael; Andres Yebra, Jose Luis; Fàbrega Canudas, Josep; Fiol Mora, Miquel Àngel; Pelayo Melero, Ignacio Manuel; Serra Albo, Oriol
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  • Edge-decompositions of K {n,n} into isomorphic copies of a given tree

     Llado Sanchez, Anna; López Masip, Susana Clara
    Journal of graph theory
    Date of publication: 2005-01
    Journal article

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  • Minimum tree decompositions with a given tree as a factor

     Llado Sanchez, Anna; López Masip, Susana Clara
    The australasian journal of combinatorics
    Date of publication: 2005-02
    Journal article

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  • Minimum degree and minimum number of edge-disjoint trees

     Llado Sanchez, Anna; López Masip, Susana Clara
    Discrete mathematics
    Date of publication: 2004-05
    Journal article

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  • DESCOMPOSICIONS DE GRAFS EN ARBRES.  Open access

     López Masip, Susana Clara
    Defense's date: 2003-02-20
    Department of Applied Mathematics IV, Universitat Politècnica de Catalunya
    Theses

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  • Decompositions of graphs with a given tree

     Llado Sanchez, Anna; López Masip, Susana Clara
    Jornadas de Matemática Discreta y Algorítmica
    Presentation's date: 2002
    Presentation of work at congresses

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  • Higher edge-connectivities and tree decompositions in regular graphs

     Gutiérrez, Amauri; Llado Sanchez, Anna; López Masip, Susana Clara
    Discrete mathematics
    Date of publication: 2000-03
    Journal article

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  • The tree decomposition number of dense graphs

     Llado Sanchez, Anna; López Masip, Susana Clara
    Date: 1999-07
    Report

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  • DECOMPOSITION OF DENSE REGULAR GRAPHS INTO TREES

     Gutiérrez, Amauri; Llado Sanchez, Anna; López Masip, Susana Clara
    British Combinatorial Conference
    Presentation's date: 1997-07-07
    Presentation of work at congresses

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  • Optimización de redes de interconexión: Transporte y difusión de la información, modelos y algoritmos. (Ref.: TIC97-0963)

     Fàbrega Canudas, Josep; Andres Yebra, Jose Luis; Balbuena Martinez, Maria Camino Teofila; Simo Mezquita, Ester; Carmona Mejias, Angeles; Martí Farré, Jaume; Garriga Valle, Ernest; Brunat Blay, Josep Maria; Saez Moreno, German; Espona Dones, Margarida; Serra Albo, Oriol; Martin Mollevi, Sebastia; Gomez Marti, Jose; Comellas Padro, Francesc de Paula; Mitjana Riera, Margarida; Padro Laimon, Carles; Maureso Sanchez, Montserrat; Fiol Mora, Miquel Àngel; Llado Sanchez, Anna; Aguilo Gost, Francisco de Asis Luis; Barriere Figueroa, Eulalia; López Masip, Susana Clara; Muñoz Lopez, Francisco Javier; Massana Hugas, Immaculada; Ozon Gorriz, Francisco Javier; Villar Santos, Jorge Luis; Zaragoza Monroig, Maria Luisa
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  • On the tree number of dense graphs

     Llado Sanchez, Anna; López Masip, Susana Clara
    Date: 1997-09
    Report

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