The Rupture Degree of <i>k</i>-Uniform Linear Hypergraph

Abstract

We employ graph parameter, the rupture degree, to measure the vulnerability of k -uniform hypergraph G k . For the k-uniform hypergraph G k underlying a non-complete graph G = ( V , E ), its rupture degree r ( G k ) is defined as r ( G k ) = max{ ω ( G k - X ) - | X | - m ( G k - X ): X &#8834; V ( G k ), ω ( G k - X ) > 1}, where X is a cut set (or destruction strategy) of G k , ω ( G k - X ) and m ( G k - X ) denote the number of components and the order of a largest component in G k - X , respectively. It is shown that this parameter can be used to measure the vulnerability of networks. In this paper, the rupture degrees of several specific classes of k -uniform hypergraph are determined.