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Article Dans Une Revue Discrete Applied Mathematics Année : 2015

Saturated boundary k-alliances in graphs

Résumé

In this paper, we introduce a new concept of saturated vertices for the alliances. For a given graph G=(V,E)G=(V,E) and S⊂VS⊂V, a vertex v∈Vv∈V is said to be SS-saturated , if the number of its defenders is equal to the number of its attackers for SS. We define new parameters |λ(S)||λ(S)| and View the MathML source|λ̄(S)| as the number of SS-saturated vertices and not SS-saturated vertices of SS, respectively. We study mathematical properties of (global) saturated boundary defensive, offensive and powerful kk-alliances and theoretical results are obtained by giving in particular some tight bounds and exact values on the cardinality of such alliances. As a main result, we give tight bounds for the cardinality of every minimal global boundary powerful (−1)(−1)-alliance (MGBPA) in terms only of the order and the size of graph. Furthermore, we establish two algorithms which generate graphs containing (connected) MGBPA from a given complete graph K2nK2n.

Dates et versions

hal-01281792 , version 1 (02-03-2016)

Identifiants

Citer

Hachem Slimani, Hamamache Kheddouci. Saturated boundary k-alliances in graphs. Discrete Applied Mathematics, 2015, 185, pp. 192-207. ⟨10.1016/j.dam.2014.11.030⟩. ⟨hal-01281792⟩
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