摘要:
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
满足以下两个条件：(i) 对于任意的顶点v∈V，均有f[v]≥1成立；(ii) 如果对任意的顶点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γ
sR(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特殊图类2⋅C
n的符号罗马控制数的精确值。
Abstract:
Let G=(V,E) be a simple undirected graph and denotes f(S)=∑
v∈sf(v) for S⊆V. A signed Roman domination function
satisfying the conditions that (i) f[v]≥1 for any v∈V, and (ii) 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 γ
sR(G)=min{f(V)|f is a signed Roman function domination f of G}. In this paper, we determine exact values of the signed Roman domination number of a special graph 2⋅C
n by constructive method and exhaustive method.