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arXiv · 2407.01121

On well (edge) dominated and equimatchable strong product graphs

Yixin Cao·Guiqiang Mou·Jianxin Wang
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Abstract

A graph is well-(edge-)dominated if every minimal (edge) dominating set is minimum. A graph is equimatchable if every maximal matching is maximum. We study these concepts on strong product graphs. We fully characterize well-edge-dominated and equimatchable strong product graphs of nontrivial graphs, and identify a large family of graphs whose strong products with any well-dominated graph are well-dominated.

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Yixin Cao, Guiqiang Mou, Jianxin Wang. 2024-07-01. On well (edge) dominated and equimatchable strong product graphs. https://arxiv.org/abs/2407.01121

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