In this paper, we establish the maximum number of basic shortest paths in Cartesian product graphs and bounds on the maximum number of the vertex-disjoint sh...

The \(P_k\)-hitting set problem consists in removing a minimum number \(\psi_k(G)\) of vertices of a given graph \(G\) so that the resulting graph does...

For the last decades, community detection is a well-studied problem because it has applications in various fields. Variable Neighborhood Search (VNS) is an e...

Let \(\gamma(G)\) and \(\iota(G)\) be the domination and independent domination numbers of a graph \(G\), respectively. In this paper, we define the ...

Distance measures play an important role in data analysis, mainly for clustering purpose, but also for data representation (for instance using multidimension...

Any telecommunication network is subject to a node or link failure at any given time. Such a failure may impact the quality of the services provided by the n...

The vertex cover problem and the dominating set problem are two well-known problems in graph theory. Their goal is to find the minimum size of a vertex subse...

Considering a graph as a network of resistances, Klein and Randić (1993) proposed the definition of a distance measure. Indeed, if each edge of the graph re...

In this paper, we propose a new scheme for building algorithms to detect communities in networks. This new approach is based upon a vertex centrality measur...

Let \(\gamma(G)\) and \(\iota(G)\) be the domination and independent domination numbers of a graph \(G\), respectively. Introduced by Sumner and Moorer...

In the literature, graphs are often studied in terms of invariants, for instance the number of vertices or edges, the stability number, the chromatic number ...

Deux colorations des sommets d'un graphe sont dites équivalentes si elles correspondent à la même partition de l'ensemble des sommets en classes de couleurs....