Conditional [formula omitted]-matching preclusion for [formula omitted]-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 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. [ABSTRACT FROM AUTHOR]