Matching preclusion for k-ary n-cubes with odd k≥3

The matching preclusion number of a graph is the minimum number of edges whose deletion results the remaining graph that has neither perfect matchings nor almost perfect matchings. In this paper, we prove that the matching preclusion number of k-ary n-cubes is 4n−1 except k=3 and n=2, where k is odd and k≥3.