摘要
设图G=(V,E)是一个简单无向图,若实值函数f:V→{-1,1,2}满足以下两个条件:(i)对于任意v∈V,均有∑_(u∈N[v])f(u)≥1成立;(ii)任意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.定义图的符号罗马控制数为γSR(G)=min{f(V)f是图G的符号罗马控制函数}.通过对完全多部图中的顶点数进行分类,给出了当k≥3时,完全多部图K(n_1,…,n_i,…,n_k)的符号罗马控制数的准确值.
A signed Roman domination function, of a simple undirected graph G=(V,E)is a function f :V→{-1,1,2} satisfying the conditions that (i)∑u∈N[v]f(u)≥1 for any v∈V, and(ii)every vertex v for which f(v)=-1 is adjacent to a vertex u for which f(u)=2. The signed roman domination number of G is γSR(G)=min{f(V) f is the signed roman domination of G}. In this paper, we compute the exact values of the signed roman domination numbers of complete multi-partite graph when k>=3, through classification the vertex of G.
引文
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