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Global alliances and independence in trees

100%

Chellali M., Haynes T.

Discussiones Mathematicae Graph Theory

2007

tom 27

nr 1

19-27

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.

Spectral study of alliances in graphs

100%

Rodríguez-Velazquez J., Almira J.

Discussiones Mathematicae Graph Theory

2007

tom 27

nr 1

143-157

In this paper we obtain several tight bounds on different types of alliance numbers of a graph, namely (global) defensive alliance number, global offensive alliance number and global dual alliance number. In particular, we investigate the relationship between the alliance numbers of a graph and its algebraic connectivity, its spectral radius, and its Laplacian spectral radius.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Almira J.

1 Chellali M.

1 Haynes T.

1 Rodríguez-Velazquez J.

2 2007

Wyniki wyszukiwania

Global alliances and independence in trees

Spectral study of alliances in graphs