Conditional k-matching preclusion for n-dimensional torus networks

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 v...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 353; pp. 181 - 190
Main Authors Hu, Xiaomin, Ren, Xiangyu, Yang, Weihua
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.08.2024
Subjects
Conditional k-matching preclusion
Fractional matching preclusion
k-matching preclusion
Matching preclusion
Tours networks
Tours networks
Conditional k-matching preclusion
Matching preclusion
Fractional matching preclusion
k-matching preclusion
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Summary: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.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2024.04.026