两类图的符号星控制数

The Signed Star Domination Numbers for two Kinds of Graph

设G=(V,E)是一个没有孤立顶点的图,一个函数f:E→{+1,-1}满足∑e∈E(v)f(e)≥1对一切v∈V(G)都成立,则称f为图G的一个符号星控制函数。图G的符号星控制数γ'ss(G)定义为γ'ss(G)=min{∑e∈E(G)f(e)︱f为图G的符号星控制函数}。以下主要确定了广义轮图及广义扇形图的符号星控制数。

Let G = （ V, G） be a graph without isolated vertices, a function f：E→{＋1,-1} is said to be the signed star dominating function （SSDF） of G if ∑f（e）≥1 holds for every υ∈V（G） The signed star domination numbers γ＇ss （G） of G is defined as γ＇ss（G）=min{∑e∈E（G）f（e） ｜f is a SSDF of G}.On the basis of the concept of signed star domination in graphs, then the followings get the signed star domination numbers for generalized wheel and generalized fan graphs.