Abstract Foucaud et al.(2022) recently introduced and initiated the study of a new graph-
theoretic concept in the area of network monitoring. For a set M of vertices and an edge e of …

We introduce a new graph-theoretic concept in the area of network monitoring. In this area,
one wishes to monitor the vertices and/or the edges of a network (viewed as a graph) in …

Abstract Foucaud, Krishna and Ramasubramony Sulochana recently introduced the concept
of monitoring edge-geodetic sets in graphs, and a related graph invariant. These are sets of …

We introduce a new graph-theoretic concept in the area of network monitoring. A set M of
vertices of a graph G is a distance-edge-monitoring set if for every edge e of G, there are a …

In order to model certain social network problems, the strong geodetic problem and its
related invariant, the strong geodetic number, are introduced. The problem is conceptually …

A path is isometric if it is a shortest path between its endpoints. In this article, we consider the
graph covering problem Isometric Path Cover, where we want to cover all the vertices of the …

The strong geodetic problem is a recent variation of the classical geodetic problem. For a
graph G, its strong geodetic number sg (G) sg (G) is the cardinality of a smallest vertex …

A monitoring edge-geodetic set, or simply an MEG-set, of a graph G is a vertex subset M⊆ V
(G) such that given any edge e of G, e lies on every shortest uv path of G, for some u, v∈ M …

Covering problems belong to the foundation of graph theory. There are several types of
covering problems in graph theory such as covering the vertex set by stars (domination …

Given a graph, a geodetic set (resp. edge geodetic set) is a subset of its vertices such that
every vertex (resp. edge) of the graph is on a shortest path between two vertices of the …