Conditional Matching Preclusion for Folded Hypercubes

Abstract

Let G be a graph with an even number of vertices. The matching preclusion number of G is the minimum number of edges whose deletion leaves the resulting graph without a perfect matching, and the conditional matching preclusion number of G is the minimum number of edges whose deletion results in a graph with no isolated vertices and without a perfect matching. Matching preclusion number was introduced for measuring the robustness of a network when there is a link failure. In this paper, we focus on conditional matching preclusion for folded hypercube FQn, an important variant of hypercube. We show that conditional matching preclusion number of FQn is 2n and all optimal conditional matching preclusion sets are trivial for n ⩾ 5.