Fractional Matching Preclusion for Möbius Cubes

Abstract

Let F be an edge subset and F′ a subset of vertices and edges of a graph G. If G − F and G − F′ have no fractional perfect matchings, then F is a fractional matching preclusion (FMP) set and F′ is a fractional strong matching preclusion (FSMP) set of G. The FMP (FSMP) number of G is the minimum size of FMP (FSMP) sets of G. In this paper, we study the fractional matching preclusion number and the fractional strong matching preclusion number for the Möbius cube MQn. In adddition, all the optimal fractional strong preclusion sets of these graphs are categorized.