关于图的符号路控制数

On Signed Path Domination in Graphs

引入了图的符号路控制的概念,给出了图G的符号路控制数γ′p(G)的一个下界,证明了γ′p(T)1对任何非平凡的树T成立,确定了完全图、圈、完全多部图和轮图的符号路控制数,并提出了若干未解决的问题和猜想.

In this paper we introduce the concept of signed path domination in graphs,give a lower bound for the signed path domination number γ~′_P(G) of a graph G,prove that γ~′_(T)1 holds for any non-trivial tree T,and determine the signed path domination numbersfor the complete t-partite graphs、cycles and wheels.In addition,we pose some open problems and conjectures.