Connectivity and matching preclusion for leaf-sort graphs

Title: Connectivity and matching preclusion for leaf-sort graphs
Creator: Wang, Shiying; Wang, Yanling; Wang, Mujiangshan
Relation: Journal of Interconnection Networks Vol. 19, Issue 3, no. 1940007
Publisher Link: http://dx.doi.org/10.1142/S0219265919400073
Publisher: World Scientific Publishing
Resource Type: journal article
Date: 2019
Description: A multiprocessor system and interconnection network have a underlying topology, which is usually presented by a graph, where nodes represent processors and links represent communication links between processors. 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. In this paper, we prove that (1) the connectivity (edge connectivity) of the leaf-sort graph CFₙ is 3n−3/2 (3n−3/2) for odd n and 3n−4/2(3n−4/2) for even n; (2) CFₙ is super edge-connected; (3) the matching preclusion number of CFₙ is 3n−3/2 for odd n and 3n−4/2 for even n; (4) the conditional matching preclusion number of CFₙ is 3n – 5 for odd n and n ≥ 3, and 3n – 6 for even n and n ≥ 4.
Subject: interconnection network; perfect matching; almost perfect matching; leaf-sort graph
Identifier: http://hdl.handle.net/1959.13/1448289
Identifier: uon:43361
Identifier: ISSN:0219-2659
Language: eng
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