Strong matching preclusion for non-bipartite torus networks

The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in the remaining graph that has neither perfect matchings nor almost perfect matchings. The torus network is one of the most popular interconnection network topologies for massively parallel computing systems because of its desirable properties. It is known that bipartite torus networks have low strong matching preclusion numbers. Hu et al. [13] proved that non-bipartite torus networks with an odd number of vertices have good strong matching preclusion properties. To complete the study of strong matching preclusion problem for non-bipartite torus networks, in this paper, we establish the strong matching preclusion number and classify all optimal strong matching preclusion sets for the n-dimensional non-bipartite torus network with an even number of vertices, where n≥3.