On well (edge) dominated and equimatchable strong product graphs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866914853358141440 |
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| author | Cao, Yixin Mou, Guiqiang Wang, Jianxin |
| author_facet | Cao, Yixin Mou, Guiqiang Wang, Jianxin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_01121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On well (edge) dominated and equimatchable strong product graphs Cao, Yixin Mou, Guiqiang Wang, Jianxin Combinatorics 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. |
| title | On well (edge) dominated and equimatchable strong product graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2407.01121 |