Conditional matching preclusion sets for an mixed-graph of the star graph and the bubble-sort graph

Abstract

The conditional matching preclusion number of a graph is the minimum number of edges, whose deletion results in a graph with no isolated vertices that has neither perfect matchings nor almost-perfect matchings. Any such optimal set is called an optimally conditional matching preclusion set. The conditional matching preclusion number is one of the parameters to measure the robustness of interconnection networks in the event of edge failure. The star graph and the bubble-sort graph are one of the attractive underlying topologies in a multiprocessor system. In this paper, we investigate a class of Cayley graphs which are combined with the star graph and the bubble-sort graph, and give all the optimally conditional matching preclusion sets for this class of graphs.