The edge-tenacity of a graph G(V,E) is denned as min{(|S|+T(G-S))/ω(G-S):S(?)E(G)},where T(G ?S) and ω(G-S), respectively, denote the order of the largest component and the number of the components of G-S. This is a...The edge-tenacity of a graph G(V,E) is denned as min{(|S|+T(G-S))/ω(G-S):S(?)E(G)},where T(G ?S) and ω(G-S), respectively, denote the order of the largest component and the number of the components of G-S. This is a better parameter to measure the stability of a network G, as it takes into account both the quantity and the order of components of the graph G-S. In a previous work, we established a necessary and sufficient condition for a graph to be edge-tenacious. These results are applied to prove that K-trees are strictly edge-tenacious. A number of results are given on the relation of edge-tenacity and other parameters, such as the higher-order edge toughness and the edge-toughness.展开更多
基金SuppoSed by the Ministry of Communication(200332922505) the Doctoral Foundation of Ministry of Education(20030151005)
文摘The edge-tenacity of a graph G(V,E) is denned as min{(|S|+T(G-S))/ω(G-S):S(?)E(G)},where T(G ?S) and ω(G-S), respectively, denote the order of the largest component and the number of the components of G-S. This is a better parameter to measure the stability of a network G, as it takes into account both the quantity and the order of components of the graph G-S. In a previous work, we established a necessary and sufficient condition for a graph to be edge-tenacious. These results are applied to prove that K-trees are strictly edge-tenacious. A number of results are given on the relation of edge-tenacity and other parameters, such as the higher-order edge toughness and the edge-toughness.
