R-Domination in Graphs

Abstract

The problem of finding a minimum k-basis of graph G is that of selecting as small a set B of vertices as possible such that every vertex of G is at distance k or less from some vertex in B. Cockayne, Goodman, and Hedetniemi previously developed a linear algorithm to find a minimum 1-basis (a minimum dominating set) when G is a tree. In this paper the k-basis problem is placed in a more general setting, and a linear algorithm is presented that solves the problem for any forest. © 1976, ACM. All rights reserved.