Coalition of cubic graphs of order at most $10$

Alikhani, Saeid; Golmohammadi, Hamidreza; Konstantinova, Elena V.

doi:10.22049/cco.2023.28328.1507

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	Coalition of cubic graphs of order at most $10$
Communications in Combinatorics and Optimization
مقاله 4، دوره 9، شماره 3، آذر 2024، صفحه 437-450 اصل مقاله (422.59 K)
نوع مقاله: Original paper
شناسه دیجیتال (DOI): 10.22049/cco.2023.28328.1507
نویسندگان
Saeid Alikhani^* ¹؛ Hamidreza Golmohammadi²^{، 3}؛ Elena V. Konstantinova²^{، 3}
¹Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran
²Novosibirsk State University, Pirogova str. 2, Novosibirsk, 630090, Russia
³Sobolev Institute of Mathematics, Ak. Koptyug av. 4, Novosibirsk, 630090, Russia
چکیده
The coalition in a graph $G$ consists of two disjoint sets of vertices $V_{1}$ and $V_{2}$, neither of which is a dominating set but whose union $V_{1}\cup V_{2}$, is a dominating set. A coalition partition in a graph $G$ is a vertex partition $\pi$ = $\{V_1, V_2,\dots, V_k \}$ such that every set $V_i \in \pi$ is not a dominating set but forms a coalition with another set $V_j\in \pi$ which is not a dominating set. The coalition number $C(G)$ equals the maximum $k$ of a coalition partition of $G$. In this paper, we compute the coalition numbers of all cubic graphs of order at most $10$.
کلیدواژه‌ها
Coalition؛ cubic graphs؛ Petersen graph

مراجع
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Coalition of cubic graphs of order at most $10$