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arXiv · 1502.01442

Matching preclusion for vertex-transitive networks

Qiuli Li·Jinghua He·Heping Zhang
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Abstract

In interconnection networks, matching preclusion is a measure of robustness when there is a link failure. Let $G$ be a graph of even order. The matching preclusion number $mp(G)$ is defined as the minimum number of edges whose deletion results in a subgraph without perfect matchings. Many interconnection networks are super matched, that is, their optimal matching preclusion sets are precisely those induced by a single vertex. In this paper, we obtain general results of vertex-transitive graphs including many known networks. A $k$-regular connected vertex-transitive graph has matching preclusion number $k$ and is super matched except for six classes of graphs. From this many previous results can be directly obtained and matching preclusion for some other networks, such as folded $k$-cubes, Hamming graphs and halved $k$-cubes, are derived.

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Qiuli Li, Jinghua He, Heping Zhang. 2015-02-05. Matching preclusion for vertex-transitive networks. https://arxiv.org/abs/1502.01442

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