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  • Publication . Conference object . 2010
    Open Access English
    Authors: 
    Moreno Casablanca, Rocío; Diánez Martínez, Ana Rosa; García Vázquez, Pedro;
    Publisher: Iniciativa Digital Politècnica
    Country: Spain

    The toughness of a noncomplete graph G is defined as τ (G) = min{|S|/ω(G − S)}, where the minimum is taken over all cutsets S of vertices of G and ω(G − S) denotes the number of components of the resultant graph G − S by deletion of S. In this paper, we investigate the ...

  • Open Access
    Authors: 
    Delia Garijo; Andrew Goodall; Jaroslav Nešetřil;
    Publisher: Elsevier BV

    We introduce a new property of graphs called ‘q-state Potts unique-ness’ and relate it to chromatic and Tutte uniqueness, and also to ‘chromatic–flow uniqueness’, recently studied by Duan, Wu and Yu. We establish for which edge-weighted graphs H homomor-phism functions ...

  • Publication . Article . 2011
    Open Access
    Authors: 
    Rocío Moreno Casablanca; A. Diánez; P. García-Vázquez;
    Publisher: Informa UK Limited

    The toughness of a non-complete graph G = (V , E) is defined as τ (G) = min{|S|/ω(G − S)}, where the minimum is taken over all cutsets S of vertices of G and ω(G − S) denotes the number of components of the resultant graph G − S by deletion of S. The corona of two graph...

  • Open Access English
    Authors: 
    José Cáceres; Delia Garijo; María Luz Puertas; Carlos Seara;
    Country: Spain

    This paper initiates a study on the problem of computing the difference between the metric dimension and the determining number of graphs. We provide new proofs and results on the determining number of trees and Cartesian products of graphs, and establish some lower bou...

  • Open Access
    Authors: 
    Camino Balbuena; Alberto Márquez; José R. Portillo;
    Publisher: Springer Science and Business Media LLC
    Country: Spain

    The Erdös–Sós conjecture says that a graph G on n vertices and number of edges e(G) > n(k − 1)/2 contains all trees of size k. In this paper we prove a sufficient condition for a graph to contain every tree of size k formulated in terms of the minimum edge degree ξ(G) o...