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## Opuscula Mathematica

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### Global offensive k-alliance in bipartite graphs

Autorzy Chellali, M.  Volkmann, L.
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
Abstrakty
 EN Let k ≥ 0 be an integer. A set S of vertices of a graph G = (V (G), E(G)) is called a global offensive k-alliance if /N(v) ∩ S/ ≥ /N(v) - S/ + k for every v ∈ V (G) - S, where 0 ≤ k Δ and Δ is the maximum degree of G. The global offensive k-alliance number [formula] is the minimum cardinality of a global offensive k-alliance in G. We show that for every bipartite graph G and every integer k ≥ 2, [formula], where Lk(G) is the set of vertices of degree at most k - 1. Moreover, extremal trees attaining this upper bound are characterized.
Słowa kluczowe
 EN global offensive k-alliance number   bipartite graphs   trees
Wydawca AGH University of Science and Technology Press
Czasopismo Opuscula Mathematica
Rocznik 2012
Tom Vol. 32, no. 1
Strony 83--89
Opis fizyczny Bibliogr. 5 poz.
Twórcy
 autor Chellali, M. autor Volkmann, L. University of Blida LAMDA-RO Laboratory, Department of Mathematics B.P. 270, Blida, Algeria, m_chellali@yahoo.com
Bibliografia
[1] M. Blidia, M. Chellali, L. Volkmann, Some bounds on the p-domintion number in trees, Discrete Math. 306 (2006), 2031–2037.
[2] M. Chellali, Offensive alliances in bipartite graphs, J. Combin. Math. Combin. Comput. 73 (2010), 245–255.
[3] P. Kristiansen, S.M. Hedetniemi, S.T. Hedetniemi, Alliances in graphs, J. Combin. Math. Combin. Comput. 48 (2004), 157–177.
[4] K.H. Shafique, R.D. Dutton, Maximum alliance-free and minimum alliance-cover sets, Congr. Numer. 162 (2003), 139–146.
[5] K.H. Shafique, R. Dutton, A tight bound on the cardinalities of maximum alliance-free and minimum alliance-cover sets, J. Combin. Math. Combin. Comput. 56 (2006), 139–145.
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