Matching preclusion for n-dimensional torus networks

The matching preclusion number of a graph is the minimum number of edges whose deletion results in the remaining graph that has neither perfect matchings nor almost perfect matchings. Wang et al. [13] proved that a class of n-dimensional tours networks with even order are super matched. Later, Cheng et al. [8] further showed that all n-dimensional tours networks with even order are super matched. In this paper, we prove that all n-dimensional torus networks with odd order are super matched if n≥3. Two-dimensional torus networks with odd order is maximally matched except for C3□C3. Our results are complementary to those of Wang et al. [13] and Cheng et al. [8].