Fractional matching preclusion of product networks

Abstract

The matching preclusion number of a graph, introduced in [2] as a fault analysis, is the minimum number of edges whose deletion leaves a resulting graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu [14] recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number of graph is the minimum number of edges whose deletion results in a graph that has no fractional perfect matching. If the sets of edges of the graph attaining the minimum are precisely those incident to a single vertex of minimum degree, we say such graph is fractional super matched. In this paper, the upper and lower bounds for the fractional matching preclusion number for Cartesian product, direct product, strong product, and lexicographic product are obtained, and we give sufficient conditions for such graphs to be fractional super matched.