关于图连通k-控制数的若干结果

Several results on connected k-domination in graphs

设G为连通图,γck(G)表示G的连通k-控制数,讨论了γck(G)的上下界,并证明了γck(G)≤2k+k+12irk(G)-2k,其中irk(G)是图G的k-无赘数.

Let G be a connected graph. γ~c_ k(G) denotes the connected k-domination number. The upper and lower bounds of γ~c_ k(G) are given and it is proved that γ~c_ k(G)≤2k+k+12ir_ k(G)-2k, where ir_ k(G) is the k-irredundance number of G.