Elsevier

Discrete Mathematics

Volume 212, Issues 1–2, 6 February 2000, Pages 149-160
Discrete Mathematics

αk- and γk-stable graphs

https://doi.org/10.1016/S0012-365X(99)00216-2Get rights and content
Under an Elsevier user license
open archive

Abstract

A set I of vertices of a graph G is k-independent if the distance between every two vertices of I is at least k+1. The k-independence number, αk(G), is the cardinality of a maximum k-independent set of G. A set D of vertices of G is k-dominating if every vertex in V(G)−D is at distance at most k from some vertex in D. The k-domination number, γk(G), is the cardinality of a minimum k-dominating set of G. A graph G is αk-stable (γk-stable) if αk(Ge)=αk(G) (γk(Ge)=γk(G)) for every edge e of G. We establish conditions under which a graph is αk- and γk-stable. In particular, we give constructive characterizations of αk- and γk-stable trees.

Keywords

Independence
Domination
Bondage number

Cited by (0)