Strong matching preclusion problem of the folded Petersen cube*

ABSTRACT A strong matching preclusion set in a graph is a set of vertices and edges whose removal leaves the graph with no perfect matchings or almost perfect matchings. The strong matching preclusion number of a graph is the minimum cardinality of a strong matching preclusion set. The notion of strong matching preclusion was introduced by Park and Ihm as an extension of the matching preclusion problem, where only edges may be deleted. The folded Petersen cubes are a class of interconnection networks, formed by iterated Cartesian products of the well-known Petersen graph and the complete graph , which possess many desirable properties. In this paper, we find the strong matching preclusion number of the folded Petersen cubes and categorize all optimal strong matching preclusion sets of these graphs. To do so, we develop and utilize more general results related to strong matching preclusion for graphs formed by Cartesian products of particular graphs.