In the current economic climate, law enforcement agencies are facing resource shortages.
The effective and efficient use of scarce resources is therefore of the utmost importance to …

The strong geodetic number, sg (G), sg (G), of a graph G is the smallest number of vertices
such that by fixing a suitable geodesic between each pair of selected vertices, all vertices of …

The strong geodetic problem on a graph G is to determine a smallest set of vertices such that
by fixing one shortest path between each pair of its vertices, all vertices of G are covered. To …

In this paper we prove that it is NP-complete to decide whether a graph can be partitioned
into nontrivial convex sets. We show that it can be verified in polynomial time whether a …

Given a graph $ G $ and a set $ S\subseteq V (G) $, we say that $ S $ is $\Delta $-convex if
the neighborhood of every vertex not in $ S $ is an independent set. A collection ${\cal …

In this paper we present further studies of convex covers and convex partitions of graphs. Let
G be a finite simple graph. A set of vertices S of G is convex if all vertices lying on a shortest …

The general notion of convexity also applies to a graph G=(V, E). A subset V c of V is called
a convex set if all shortest paths with end vertices in V c remain within V c. A convex cut of G …

A binary linear programming (BLP) formulation of graph convex covering problems is
proposed for the first time. Since the general convex covering problem of a graph is NP …

Cette thèse porte sur le problème de la couverture d'ensembles finis dans une structure
discrète. Cette problématique très générale permet de nombreuses approches et nous …

Диссертация выполнена в Молдавском Госуниверситете, Кишинёв, 2017 год. Структура
работы: Диссертация написана на румынском языке и содержит введение, три главы …