科研之友
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摘要
A function f : V(G) --> {+1, -1} defined on the vertices of a graph G is a signed dominating function if for any vertex v the sum of function values over its closed neighborhood is at least 1. The signed domination number gamma(s)(G) of G is the minimum weight of a signed dominating function oil G. By simply changing "{+1, -1}" in the above definition to "{+ 1. 0, -1}", we can define the minus dominating function and the minus domination number of G. In this note, by applying the Turan theorem, we present sharp lower bounds on the signed domination number for a graph containing no (k + 1)-cliques. As a result, we generalize a previous result due to Kang et al. on the minus domination number of k-partite graphs to graphs containing no (k + 1)-cliques and characterize the extremal graphs.
