论文标题
在一棵树的互补棱镜的凸数中
On the convexity number of the complementary prism of a tree
论文作者
论文摘要
图$ g $的一组顶点$ s $是（地理）凸集，如果$ s $包含所有属于$ s $两个顶点之间任何最短路径的所有顶点。 $ g $的最大适当凸的基数称为凸数，$ g $的con $（g）$。 $ g $的互补棱镜$ g \ bar {g} $是从$ g $的不相交联合及其补充$ \ bar {g} $获得的，通过添加它们之间的完美匹配的边缘。在这项工作中，我们研究了树木的互补棱镜的凸组，并为所有树木的互补棱镜的凸数数字提供了公式。
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.
