Journal
COMPUTER JOURNAL
Volume 65, Issue 7, Pages 1874-1890Publisher
OXFORD UNIV PRESS
DOI: 10.1093/comjnl/bxab029
Keywords
interconnection network; matching preclusion; enhanced hypercube
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Funding
- National Natural Science Foundation of China [61772010]
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This paper investigates the matching preclusion number and the strong matching preclusion number of the enhanced hypercube, providing specific values for each.
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 <= k <= 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 <= k <= n- 1), the strong matching preclusion number of Q(n,k) is n +1 (2 <= k <= n-1), the conditional matching preclusion number of Qn, n-1 is 2n- 1, the conditional matching preclusion number of Q(n,k) is 2n (1 <= k <= n - 2) and the conditional strong matching preclusion number of Q(n,n)-2 is 2n - 3 (n >= 4).
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