On well-edge-dominated graphs
| Autor: | Anderson, Sarah E., Kuenzel, Kirsti, Rall, Douglas F. |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | A graph is said to be well-edge-dominated if all its minimal edge dominating sets are minimum. It is known that every well-edge-dominated graph $G$ is also equimatchable, meaning that every maximal matching in $G$ is maximum. In this paper, we show that if $G$ is a connected, triangle-free, nonbipartite, well-edge-dominated graph, then $G$ is one of three graphs. We also characterize the well-edge-dominated split graphs and Cartesian products. In particular, we show that a connected Cartesian product $G\Box H$ is well-edge-dominated, where $G$ and $H$ have order at least $2$, if and only if $G\Box H = K_2 \Box K_2$. Comment: 18 pages, 2 figures, 18 references |
| Databáze: | arXiv |
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