International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1990 / Article

Open Access

Volume 13 |Article ID 796320 | 2 pages | https://doi.org/10.1155/S016117129000031X

A note on the k-domination number of a graph

Received30 Dec 1988
Revised01 Feb 1989

Abstract

The k-domination number of a graph G=G(V,E), γk(G), is the least cardinality of a set XV 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+1nk1, n1, k1 then, γk(G)npn+1, where p is the order of G.

Copyright © 1990 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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