Author(s)

Ning Zhao

Department of Mathematics and Statistics, Qinghai Minzu University, Xining, China.

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 ⊂ 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.

The Rupture Degree, Hypergraph, k-Uniform Linear Hypergraph

Zhao, N. (2021) The Rupture Degree of k-Uniform Linear Hypergraph. Applied Mathematics, 12, 556-562. doi: 10.4236/am.2021.127039.