International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 1, Pages 205-206
doi:10.1155/S016117129000031X

A note on the k-domination number of a graph

Y. Caro1 and Y. Roditty2

1Department of Mathematics, University of Haifa-Oranim, Geva 18915, Israel
 2Department of Mathematics, Beit-Berl College and School of Mathematical Sciences, Tel-Aviv University, Israel

Abstract

The k-domination number of a graph G=G(V,E), γk(G), is the least cardinality of a set X⊂V such that any vertex in VX is adjacent to at least k vertices of X.Extending a result of Cockayne, Gamble and Shepherd [4], we prove that if δ(G)≥n+1nk−1, n≥1, k≥1 then, γk(G)≤npn+1, where p is the order of G.