Global alliances and independence in trees

• Autorzy: Mustapha Chellali , Teresa W. Haynes
• Języki publikacji: EN

Abstrakty

EN

A global defensive (respectively, offensive) alliance in a graph G = (V,E) is a set of vertices S ⊆ V with the properties that every vertex in V-S has at least one neighbor in S, and for each vertex v in S (respectively, in V-S) at least half the vertices from the closed neighborhood of v are in S. These alliances are called strong if a strict majority of vertices from the closed neighborhood of v must be in S. For each kind of alliance, the associated parameter is the minimum cardinality of such an alliance. We determine relationships among these four parameters and the vertex independence number for trees.

Słowa kluczowe

EN

defensive alliance; offensive alliance; global alliance; domination; trees; independence number

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2007
• Tom: 27
• Numer: 1
• Strony: 19-27

Daty

wydano

2007

otrzymano

2004-10-04

poprawiono

2006-04-26

Twórcy

autor

Mustapha Chellali

• Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria

autor

Teresa W. Haynes

• Department of Mathematics, East Tennessee State University, Johnson City, TN 37614, USA

Bibliografia

• [1] M. Blidia, M. Chellali and O. Favaron, Independence and 2-domination in trees, Austral. J. Combin. 33 (2005) 317-327.
• [2] G. Chartrand and L. Lesniak, Graphs & Digraphs: Third Edition (Chapman & Hall, London, 1996).
• [3] E.J. Cockayne, O. Favaron, C. Payan and A.G. Thomason, Contributions to the theory of domination, independence, and irredundance in graphs, Discrete Math. 33 (1981) 249-258, doi: 10.1016/0012-365X(81)90268-5.
• [4] T.W. Haynes, S.T. Hedetniemi, and M.A. Henning, Global defensive alliances in graphs, The Electronic J. Combin. 10 (2003) R47.
• [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
• [6] T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998).
• [7] S.M. Hedetniemi, S.T. Hedetniemi and P. Kristiansen, Alliances in graphs, J. Combin. Math. Combin. Comput. 48 (2004) 157-177.

Identyfikatory

DOI

10.7151/dmgt.1340