关于树的补棱柱的凸数
On the convexity number of the complementary prism of a tree
摘要：
一个图$G$的顶点集$S$是一个（测地）凸集，如果$S$包含属于连接$S$的两个顶点之间的任何最短路的所有顶点. $G$的最大真凸集的基数称为$G$的凸数con $(G)$。$G$的互补棱柱$G\bar{G}$是由$G$和它的互补体$\bar{G}$的不相交并通过在它们之间添加完美匹配的边而获得的。在这项工作中，我们研究了一棵树的互补棱柱的凸集，并推导出公式的凸数的互补棱柱的所有树木。
英文摘要：
A set of vertices $S$ of a graph $G$ is a (geodesic)convex set, if $S$ contains all the vertices belonging to any shortest path connecting between two vertices of $S$. The cardinality of maximum proper convex set of $G$ is called the convexity number, con$(G)$ of $G$. The complementary prism $G\bar{G}$ of $G$ is obtained from the disjoint union of $G$ and its complement $\bar{G}$ by adding the edges of a perfect matching between them. In this work, we examine the convex sets of the complementary prism of a tree and derive formulas for the convexity numbers of the complementary prisms of all trees.
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