The Rupture Degree of k-Uniform Linear Hypergraph

We employ graph parameter, the rupture degree, to measure the vulnerability of k-uniform hypergraph Gk. For the k-uniform hypergraph Gk underlying a non-complete graph G = (V, E), its rupture degree r(Gk) is defined as r(Gk) = max{ω(Gk - X) - |X| - m(Gk - X): X ⊂ V(Gk), ω(Gk - X) > 1}, where X is a cut set (or destruction strategy) of Gk, ω(Gk - X) and m(Gk - X) denote the number of components and the order of a largest component in Gk - 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.