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Trees with equal global offensive k-alliance and k-domination numbers

By Mustapha. Chellali

Abstract

Tyt. z nagłówka.Bibliogr. s. 253.Dostępny również w formie drukowanej.ABSTRACT: Let k ≥ 1 be an integer. A set S of vertices of a graph G = (V (G), E(G)) is called a global offensive k-alliance if [formula] for every [formula], where N(v) is the neighborhood of v. The subset S is a k-dominating set of G if every vertex in V (G) - S has at least k neighbors in S. The global offensive k-alliance number [formula] is the minimum cardinality of a global offensive k-alliance in G and the k-domination number [formula] is the minimum cardinality of a k-dominating set of G. For every integer k ≥ 1 every graph G satisfies [formula]. In this paper we provide for k ≥ 2 a characterization of trees T with equal [formula] and [formula]. KEYWORDS: global offensive k-alliance number, k-domination number, trees

DOI identifier: 10.7494/opmath.2010.30.3.249
OAI identifier: oai:abc.krakow.pl:dd2011317135
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