Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21289320240901Coalition of cubic graphs of order at most $10$4374501454210.22049/cco.2023.28328.1507ENSaeidAlikhaniDepartment of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran0000-0002-1801-203XHamidrezaGolmohammadiNovosibirsk State University, Pirogova str. 2, Novosibirsk, 630090, RussiaSobolev Institute of Mathematics, Ak. Koptyug av. 4, Novosibirsk, 630090, RussiaElena V.KonstantinovaNovosibirsk State University, Pirogova str. 2, Novosibirsk, 630090, RussiaSobolev Institute of Mathematics, Ak. Koptyug av. 4, Novosibirsk, 630090, RussiaJournal Article20230217The 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 $10$.http://comb-opt.azaruniv.ac.ir/article_14542_103d8d93afd44cc6d45e68bdcf8227d1.pdf