论文标题
立方图的联盟最多$ 10 $
Coalition of cubic graphs of order at most $10$
论文作者
论文摘要
图$ g $中的联盟由两个不相交的顶点$ v_ {1} $和$ v_ {2} $组成，这两个都不是一个主导集，而是其Union $ v_ {1} \ Cup v_ {2} $的联合集合。图$ g $中的联盟分区是顶点分区$π$ = $ \ {v_1，v_2，...，...，v_k \} $，这样的每个集合$ v_i \ inπ$ inπ$ inπ$ inπ$不是一个统治集，而是与另一组$ v_j \ inπ$组成的联盟集合。联盟编号$ c（g）$等于$ g $的联盟分区的最大$ k $。在本文中，我们计算所有立方图的联盟数量最多为$ 10 $。
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 $π$ = $\{V_1, V_2,..., V_k \}$ such that every set $V_i \in π$ is not a dominating set but forms a coalition with another set $V_j\in π$ 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 number of all cubic graphs of order at most $10$.
