论文标题
部分可观测时空混沌系统的无模型预测
Introduction to total coalitions in graphs
论文作者
论文摘要
令$ g $为带顶点套装$ v $的图。两个不相交的集合$ v_1，v_2 \ subseteq v $称为$ g $的总联盟，如果$ v_1 $ and $ v_2 $都是$ g $的总统治集，但$ v_1 \ cup v_2 $是总的支配集。 $ g $的总联盟分区是顶点分区$π= \ {v_1，v_2，v_2，\ ldots，v_k \} $，这样一组$π$是一个总的支配集，但每个集合$ v_i \ inπ$ inπ$ inπ$ inπ$ inπ$ inπ$ inπ$ inπ$。 $ g $的总联盟分区的最大基数称为$ g $的总联盟数量，由$ tc（g）$表示。在本文中，我们启动了图表及其特性中的总联盟的研究。
Let $G$ be a graph with vertex set $V$. Two disjoint sets $V_1, V_2\subseteq V$ are called a total coalition in $G$, if neither $V_1$ and $V_2$ is a total dominating set of $G$ but $V_1\cup V_2$ is a total dominating set. A total coalition partition of $G$ is a vertex partition $π=\{V_1,V_2,\ldots, V_k\}$ such that no set of $π$ is a total dominating set but each set $V_i\in π$ forms a total coalition with another set $V_j\in π$. The maximum cardinality of a total coalition partition of $G$ is called the total coalition number of $G$, denoted by $TC(G)$. In this paper, we initiate the study of the total coalition in graphs and its properties.
