k部图的符号控制数的一个下界

A Lower Bound of Signed Domination Number of Partite Graph

研究图的符号控制数,得到了n阶k部图的符号控制数的一个下界,当δ=2时这个界是精确的,并且给出了δ=2时一个达到下界的图例.王春香等得到的结果(引言中的定理B)是本文结果当δ=2且k=2时的一个特例.

In this paper, we study the signed domination number of graphs and obtain a lower bound for a k-partite graph. This bound is sharp when δ=2. As a sample, we construct a graph with δ=2, which reaches the above lower bound. Wang Chunxiang's result γ_s(G)4(-1+1+n)-n is a special case of our results in δ=2 and k=2.