Matching Preclusion Number in Cartesian Product of Graphs and its Application to Interconnection Networks

Abstract

The matching preclusion number of a graph \(G\), denoted by \(mp(G)\), is the minimum number of edges whose deletion leaves a resulting graph that has neither perfect matchings nor almost perfect matchings. Besides its theoretical linkage with conditional connectivity and extremal graph theory, the matching preclusion number serves as a measure of robustness in interconnection networks. In this paper, we develop general properties related to matchings in the Cartesian product of graphs, enabling us to establish the matching preclusion number for various interconnection (product) networks, specifically: hyper Petersen, folded Petersen, folded Petersen cube, hyperstar, star-cube, and hypercube. Furthermore, we show that the Cartesian product of graphs operation inherits the matching preclusion number optimality from factor graphs of even order, reinforcing the Cartesian product as a desirable network-synthesizing operator.