%0 Journal Article
%T Coalition of cubic graphs of order at most $10$
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Alikhani, Saeid
%A Golmohammadi, Hamidreza
%A Konstantinova, Elena V.
%D 2024
%\ 09/01/2024
%V 9
%N 3
%P 437-450
%! Coalition of cubic graphs of order at most $10$
%K Coalition
%K cubic graphs
%K Petersen graph
%R 10.22049/cco.2023.28328.1507
%X 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 $10$.
%U http://comb-opt.azaruniv.ac.ir/article_14542_103d8d93afd44cc6d45e68bdcf8227d1.pdf