J. Sigarreta

activity

20062026

most citedGlobal defensive k-alliances in graphs

32 citations · 177 across the 37 of their papers we have counts for

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Showing 2006Show all

6 papers · 1 filter

math.CO2006★ 32 cited

Global defensive k-alliances in graphs

J. A. Rodriguez, J. M. Sigarreta

Let $Γ = (V, E)$ be a simple graph. For a nonempty set $X \subseteq V$ , and a vertex $v \in V$ , $δ_{X} (v)$ denotes the number of neighbors $v$ has in $X$ . A nonempty set $S \subseteq V$ …

math.CO2006★ 1 cited

Offensive alliances in cubic graphs

J. A. Rodriguez, J. M. Sigarreta

An offensive alliance in a graph $Γ = (V, E)$ is a set of vertices $S \subset V$ where for every vertex $v$ in its boundary it holds that the majority of vertices in $v$ 's closed neigh…

math.CO2006★ 6 cited

Spectral study of alliances in graphs

J. A. Rodriguez, J. M. Sigarreta

In this paper we obtain several tight bounds on different types of alliance numbers of a graph: (global) defensive alliance number, global offensive alliance number and global dual…

math.CO2006

On defensive alliances and line graphs

J. M. Sigarreta, J. A. Rodriguez

Let $Γ$ be a simple graph of size $m$ and degree sequence $δ_{1} \geq δ_{2} \geq ... \geq δ_{n}$ . Let $L (Γ)$ denotes the line graph of $Γ$ . The aim of this paper is to study mathematic…

math.CO2006

On the global offensive alliance number of a graph

J. M. Sigarreta, J. A. Rodriguez

An offensive alliance in a graph $Γ = (V, E)$ is a set of vertices $S \subset V$ where for every vertex $v$ in its boundary it holds that the majority of vertices in $v$ 's closed neigh…

math.CO2006★ 1 cited

Alliance free and alliance cover sets

J. A. Rodriguez-Velazquez, J. M. Sigarreta, I. G. Yero +1

A \emph{defensive} (\emph{offensive}) $k$ -\emph{alliance} in $Γ = (V, E)$ is a set $S \subseteq V$ such that every $v$ in $S$ (in the boundary of $S$ ) has at least $k$ more neighbors i…