In this paper, we study the behaviour of the generalized power domination number of a
graph by small changes on the graph, namely edge and vertex deletion and edge …

The power domination problem in graphs consists of finding a minimum set of vertices S⊆ V
that monitors the entire graph G governed by two 'monitoring rules'-domination and …

The concept of power domination emerged from the problem of monitoring electrical
systems. Given a graph G and a set S ⊆ V (G) S⊆ V (G), a set M of monitored vertices is …

Power domination in graphs emerged from the problem of monitoring an electrical system by
placing as few measurement devices in the system as possible. It corresponds to a variant of …

The Power dominating set is a minimum point of determination in a graph that can dominate
the connected dots around it, with a minimum domination point. The smallest cardinality of a …

Given a graph G=(V, E) and a set S⊆ V of vertices, we say that:(i) if a vertex v∈ S, then v
and all vertices in N (v) are observed, and (ii)(Kirchhoff's Rule) if a vertex v is observed and …

The concept of power domination emerged from the problem of monitoring electrical
systems. Given a graph G and a set S $\subseteq $ V (G), a set M of monitored vertices is …

A zero forcing set is a set S of vertices of a graph G, called forced vertices of G, which are
able to force the entire graph by applying the following process iteratively: At any particular …

Motivated by the question of computing the probability of successful power domination by
placing k monitors uniformly at random, in this paper we give a recursive formula to count …

In a graph G=(V, E), a subset D of V (G) is called a 2-dominating set if every vertex of V (G)\D
has two neighbours in D. The 2-domination number is the minimum order of such a set D …