Fractional Matching Preclusion for Folded Petersen Cube Networks

Abstract

Let F be an edge set and F′ a subset of edges and/or vertices of a graph G. Then F is a fractional matching preclusion(FMP) set (F′ is a fractional strong matching preclusion (FSMP) set) if G − F (G − F′) does not contain fractional perfect matching. The FMP(FSMP) number of G is the minimum size of FMP(FSMP) sets of G. The concept of matching preclusion was introduced by Brigham et al., as a measure of robustness in the event of edge failure in interconnection networks. An interconnection network of a larger MP number may be considered as more robust in the event of link failures. The problem of fractional matching preclusion is a generalization of matching preclusion. In this paper, we obtain the FMP and FSMP number for the folded Petersen cube networks. All the optimal fractional strong matching preclusion sets of these graphs are categorized.