关于图的符号团控制数

On Signed Clique Domination Numbers of Graphs

对于一个非空图G=(V,E)和一个函数f:E→{-1,+1},若S■E,则记f(s)=∑e∈sf(e).若对于G中每个非平凡的团K均满足f(E(K))≥1,则f被称为G的一个符号团控制函数,G的符号团控制数表达为γ′scl(G)=min{f(E)}|f为图G的符号团控制函数}.该文研究了几类联图的符号团控制数,主要确定了C_(m)K_(n)^(-)、C_(m)∨nK_(2)和C_(m)∨C_(n)的符号团控制数,从而推广了已有的部分结果.

For a nonempty graph G=(V,E)and a functionf:f:E→{-1,+1},if S■E then writef(s)=∑e∈sf(e)a functionf is said to be a signed clique dominating function(SCDF)of the graph G if(E(K))≥1 holds for every nontrivial clique K in G,and the signed clique domination number of G is defined asγ′scl(G)=min{f(E)}f is SCDF of G}.In this paper,the signed clique domination numbers of some join graph are studied,and the signed clique domination numbers of graphs C_(m)K_(n)^(-)、C_(m)∨nK_(2)and C_(m)∨C_(n)are mainly determined,which generalize partially some known results.