Fractional strong matching preclusion of some Cartesian product graphs

The fractional strong matching preclusion number of a graph is the minimum number of edges and vertices whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we obtain the fractional strong matching preclusion number for the Cartesian product of a graph and a cycle. As an application, the fractional strong matching preclusion number for torus networks is also obtained.

Fractional Strong Matching Preclusion for DHcube

Let [Formula: see text] be a set edges and [Formula: see text] be a set of edges and/or vertices of a graph [Formula: see text], then [Formula: see text] (resp. [Formula: see text]) is a fractional matching preclusion set (resp. fractional strong matching preclusion set) if [Formula: see text] (resp. [Formula: see text]) contains no fractional perfect matching. The fractional matching preclusion number (resp. fractional strong matching preclusion number) of [Formula: see text] is the minimum size of fractional matching preclusion set (resp. fractional strong matching preclusion set) of [Formula: see text]. In this paper, we obtain the fractional matching preclusion number and fractional strong matching preclusion number of the DHcube [Formula: see text] for [Formula: see text]. In addition, all the optimal fractional matching preclusion sets and fractional strong matching preclusion sets of these graphs are categorized.

Fractional Matching Preclusion for Folded Petersen Cube Networks

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.

Fractional Matching Preclusion for Restricted Hypercube-Like Graphs

The restricted hypercube-like graphs, variants of the hypercube, were proposed as desired interconnection networks of parallel systems. The matching preclusion number of a graph is the minimum number of edges whose deletion results in the graph with neither perfect matchings nor almost perfect matchings. The fractional perfect matching preclusion and fractional strong perfect matching preclusion are generalizations of the matching preclusion. In this paper, we obtain fractional matching preclusion number and fractional strong matching preclusion number of restricted hypercube-like graphs, which extend some known results.

Fractional matching preclusion for radix triangular mesh

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu recently introduced the concept of fractional matching preclusion number. The fractional matching preclusion number (FMP number) of [Formula: see text], denoted by [Formula: see text], is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The fractional strong matching preclusion number (FSMP number) of [Formula: see text], denoted by [Formula: see text], is the minimum number of vertices and edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we study the fractional matching preclusion number and the fractional strong matching preclusion number for the radix triangular mesh [Formula: see text], and all the optimal fractional matching preclusion sets and fractional strong matching preclusion sets of these graphs are categorized.

Fractional Matching Preclusion for (n, k)-Star Graphs

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost perfect matchings. As a generalization, Liu and Liu introduced the concept of fractional matching preclusion number in 2017. The Fractional Matching Preclusion Number (FMP number) of G is the minimum number of edges whose deletion leaves the resulting graph without a fractional perfect matching. The Fractional Strong Matching Preclusion Number (FSMP number) of G is the minimum number of vertices and/or edges whose deletion leaves the resulting graph without a fractional perfect matching. In this paper, we obtain the FMP number and the FSMP number for (n, k)-star graphs. In addition, all the optimal fractional strong matching preclusion sets of these graphs are categorized.