Abstract
Abstract The (conditional) matching preclusion number of a graph is the minimum number of edges whose deletion leaves the resulting graph (with no isolated vertices) that has neither perfect matchings nor almost perfect matchings. The (conditional) strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion makes the resulting graph (with no isolated vertices) without perfect matching or almost perfect matching. The enhanced hypercube $Q_{n,k}$ $(1\leq k\leq n-1)$ is an extension of hypercube. In this paper, we prove that the matching preclusion number of $Q_{n,k}$ is $n+1$ $(1\leq k\leq n-1)$, the strong matching preclusion number of $Q_{n,k}$ is $n+1$ $(2\leq k\leq n-1)$, the conditional matching preclusion number of $Q_{n,n-1}$ is $2n-1$, the conditional matching preclusion number of $Q_{n,k}$ is $2n$ $(1\leq k\leq n-2)$ and the conditional strong matching preclusion number of $Q_{n,n-2}$ is $2n-3$ $(n\geq 4)$.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
