两类冠图的符号罗马控制数

The Signed Roman Domination Number of Two Classes Corona Graph

设图G=(V,E)为一个简单无向图,若S?V,则记f(S)=∑v∈sf(v)。若实值函数f:V→{-1,1,2}满足以下两个条件:1) 对于任意的顶点v∈V,均有f(N[v])≥1成立;2) 如果对任意顶点v∈V,若f(v)=-1,则存在一个与v相邻的顶点u∈V满足f(u)=2,则称该函数为图G的符号罗马控制函数。图G的符号罗马控制数定义为γsR(G)=min{f(V)|f为图G的一个符号罗马控制函数}。本文利用构造法及穷标法主要得到了k-正则图的冠图以及轮图的冠图的符号罗马控制数的精确值。

Let G=(V,E) be a simple undirected graph and denote f(S)=∑v∈sf(v) for S?V. A real-valued function f:V→{-1,1,2} is called a signed Roman domination function if f satisfies the conditions that 1) f(N[v])≥1 for any v∈V, and 2) every vertex v for which f(v)=-1 is adjacent to a vertex u for which is f(u)=2. The signed Roman domination number of G is γsR(G)=min{f(V)|f is a signed Roman domination function f of G} . In this paper, we determine exact values of the signed Roman domination number of two classes graph, such as a Corona of k-regular graph and wheel graph by constructive method and exhaustive method.