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Spectral study of alliances in graphs

Juan Alberto Rodríguez-VelazquezJose Maria Sigarreta Almira — 2007

Discussiones Mathematicae Graph Theory

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.

Weak Total Resolvability In Graphs

Katrin CaselAlejandro Estrada-MorenoHenning FernauJuan Alberto Rodríguez-Velázquez — 2016

Discussiones Mathematicae Graph Theory

A vertex v ∈ V (G) is said to distinguish two vertices x, y ∈ V (G) of a graph G if the distance from v to x is di erent from the distance from v to y. A set W ⊆ V (G) is a total resolving set for a graph G if for every pair of vertices x, y ∈ V (G), there exists some vertex w ∈ W − {x, y} which distinguishes x and y, while W is a weak total resolving set if for every x ∈ V (G)−W and y ∈ W, there exists some w ∈ W −{y} which distinguishes x and y. A weak total resolving set of minimum cardinality...

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