Integer [formula omitted]-matching preclusion of twisted cubes and ([formula omitted])-star graphs

Abstract

An integer k-matching of a graph G is a function f from E(G) to {0,1,⋯,k} such that the sum of f(e) is not more than k for any vertex u, where the sum is taken over all edges e incident to u. When k=1, the integer k-matching is a matching. The (strong) integer k-matching preclusion number of G, denoted by mpk(G) (smpk(G)), is the minimum number of edges (vertices and edges) whose deletion results in a graph with neither perfect integer k-matching nor almost perfect integer k-matching. This is an extension of the (strong) matching preclusion problem that was introduced by Brigham, Park and Ihm et al. The twisted cubes and the (n,s)-star graphs have more desirable properties. In this paper, MPk number and SMPk number of the twisted cubes and (n,s)-star graphs are given, respectively.