Abstract
The k-matching preclusion number of a graph is the minimum number of edges whose deletion results in the remaining graph that has neither perfect k-matchings nor almost perfect k-matchings. For many networks, their optimal k-matching preclusion sets are precisely those edges incident with a single vertex. In this paper, we introduce the concept of conditional k-matching preclusion, in which isolated vertices are not permitted in fault networks. We establish the conditional k-matching preclusion numbers and all possible minimum conditional k-matching preclusion sets for n-dimensional torus networks with n≥3. In addition, we investigate the relationship between all optimal sets for three kinds of (conditional) matching preclusion problems.
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.
