In this paper we study the spectral properties of the threshold graphs. In particular, we give lower and upper bounds for the largest and smallest eigenvalue...

The energy of a graph \(G\), denoted by \({\cal E}(G)\), is defined as the sum of the absolute values of all eigenvalues of \(G\). In this paper we stu...

In the present paper, we prove lower and upper bounds for each of the ratios \(GA/\delta\), as well as a lower bound on \(GA/\sqrt{\delta}\), in terms of...

A small polygon is a polygon of unit diameter. The question of finding the largest area of small \(n-\)gons has been answered for some values of \(n\)....

The Integral Simplex Using Decomposition (ISUD) algorithm has been developed recently to solve large set partitioning problems (SPPs) in a primal way, i.e.,...

Clustering is the subject of active research in several fields such as operations research, statistics, pattern recognition, and machine learning. The range ...

Clustering is an automated and powerful technique for data analysis. It aims to divide a given set of data points into clusters which are homogeneous and/o...

Soient \({\mathcal D(G)}\), \({\mathcal D}^L(G)={\mathcal Diag(Tr)} - {\mathcal D(G)}\) et \({\mathcal D}^Q(G)={\mathcal Diag(Tr)} + {\mathcal D(G)}\),...

Soit \(G\) un graph d'ordre \(n\). L'énergie \(\mathcal{E}(G)\) d'un graph simple \(G\) est la somme de des valeurs absolues des valeurs propres de s...

Given an integer solution, the integral simplex using decomposition (ISUD) seeks a descent direction that leads to an improved adjacent integer solution. It ...

Nous donnons des conditions nécessaires et suffisante pour l'existence d'un graphe simple, ou d'un graphe connexe simple, ayant des nombres donnés `(m_{ij}...

The distance, distance Laplacian and distance signless Laplacian spectra of a connected graph \(G\) are the spectra of the distance, distance Laplacian and...

The paper discusses bounds on the nullity number of graphs. It is proved in [B. Cheng and B. Liu, On the nullity of graphs. Electron. J. Linear Algebra 16 ...

Les heuristiques basées sur la théorie des graphes sont largement utilisées dans plusieurs domaines pour résoudre approximativement des problèmes d'optimisat...

Dans cet article, nous nous intéressons à létude des valeurs propres du laplacien des distances d'un graphe connexe d'ordre \(n\) et de nombre chromatique ...

L'indice géométrique-arithmétique \(GA\) d'un graphe \(G\) est la somme des ratios, sur l'ensemble des arêtes de \(G\), de la moyenne géométrique sur l...

Dans le présent article, nous démontrons des bornes inférieure et supérieure sur chacun des rapports \(GA/\delta\), \(GA/\overline{d}\) et \(\Delta\), ...

Dans le présent article, nous comparons l'indice géométrique-arithmétique \(GA\) et le nombre chromatique \(\chi\) d'un graphe connexe d'ordre donné. Ent...

Variable neighborhood search (VNS) is a framework for building heuristics, based upon systematic changes of neighborhoods both in a descent phase, to find a...

In this paper, the first steps toward the use of the Variable Neighborhood Search metaheuristic are explained. The method is presented step by step using an...