S. Bermudo

activity

20062024

collaborators

6 papers

math.CO2024

Domination number of modular product graphs

Sergio Bermudo, Iztok Peterin, Jelena Sedlar +1

The modular product $G ⋄ H$ of graphs $G$ and $H$ is a graph on vertex set $V (G) \times V (H)$ . Two vertices $(g, h)$ and $(g^{'}, h^{'})$ of $G ⋄ H$ are adjacent…

math.CO2015

On the adjacency dimension of graphs

A. Estrada-Moreno, Y. Ramirez-Cruz, J. A. Rodriguez-Velazquez

A generator of a metric space is a set $S$ of points in the space with the property that every point of the space is uniquely determined by its distances from the elements of $S$ .…

math.CO2011

Alliance free sets in Cartesian product graphs

Ismael G. Yero, Juan A. Rodriguez-Velazquez, Sergio Bermudo

Let $G = (V, E)$ be a graph. For a non-empty subset of vertices $S \subseteq V$ , and vertex $v \in V$ , let $δ_{S} (v) = ∣ {u \in S : uv \in E} ∣$ denote the cardinality of the set of neighbors o…

math.CO2009

Partitioning a graph into defensive k-alliances

Ismael G. Yero, Sergio Bermudo, Juan A. Rodriguez-Velazquez +1

A defensive $k$ -alliance in a graph is a set $S$ of vertices with the property that every vertex in $S$ has at least $k$ more neighbors in $S$ than it has outside of $S$ . A defensi…

math.CO2008

On global offensive k-alliances in graphs

Sergio Bermudo, Juan A. Rodriguez-Velazquez, Jose M. Sigarreta +1

We investigate the relationship between global offensive $k$ -alliances and some characteristic sets of a graph including $r$ -dependent sets and $τ$ -dominating sets. As a consequenc…

math.CO2006

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…