Volume 55, Number 2, March-April 2021
|Page(s)||495 - 503|
|Published online||31 March 2021|
A lower bound on the global powerful alliance number in trees
Department of Mathematics, University of Boumerdes, Boumerdes, Algeria
2 Department of Mathematics, B.P. 270, University of Blida, Blida, Algeria
Accepted: 20 February 2021
For a graph G = (V, E), a set D ⊆ V is a dominating set if every vertex in V − D is either in D or has a neighbor in D. A dominating set D is a global offensive alliance (resp. a global defensive alliance) if for each vertex v in V − D (resp. v in D) at least half the vertices from the closed neighborhood of v are in D. A global powerful alliance is both global defensive and global offensive. The global powerful alliance number γpa(G) is the minimum cardinality of a global powerful alliance of G. We show that if T is a tree of order n with l leaves and s support vertices, then . Moreover, we provide a constructive characterization of all extremal trees attaining this bound.
Mathematics Subject Classification: 05C69 / 05C05
Key words: Domination / global powerful alliance / trees
© EDP Sciences, ROADEF, SMAI 2021
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