Conditional matching preclusion of enhanced hypercubes

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. In this paper, we prove that the $n$-dimensional enhanced hypercubes are super conditional matched with $n\ge 6$. Our work is complementary to Lin et al. and Wang et al., who proved a special case of enhanced hypercubes is super conditional matched and calculated the conditional matching preclusion number of enhanced hypercubes, respectively.