Matching preclusion number in product graphs

The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has no perfect matchings or almost-perfect matchings. For many interconnection networks, the matching preclusion number is equal to the minimum degree of a vertex in the network, and the sets of edges attaining the minimum are precisely those incident to a single vertex of minimum degree; we say such networks are super matched. In this paper we derive upper and lower bounds for the matching preclusion number for networks constructed using a variety of binary graph operations, and give sufficient conditions for such networks to be super matched. (C) 2018 Elsevier B.V. All rights reserved.