Given a graph <i>G=(V,E)</i>, the first Zagreb index <i>M</i>₁ is the sum of its vertices squared degrees and the second Zagreb index <i>M</i><sub...

Khalifeh, Yousefi-Azari, Ashrafi and Wagner [European J. Combin. 30 (2009) 1149-1163] conjectured that for a connected graph <i>G</i> on <i>n</i> vertices...

The proximity <img src="/cgi-bin/mimetex.cgi?\pi"> of a graph <i>G</i> is the minimum average distance from a vertex of <i>G</i> to all others. Similarly, th...

Given a set of entities associated with points in Euclidean space, minimum sum-of-squares clustering (MSSC) consist in partitioning this set into clusters su...

During the last three decades, the computer has been widely used in spectral graph theory. Many results about graph eigenvalues were first conjectured, and i...

It is observed that mutations in the formulations of test problems over time are not infrequent. Ensuing problems are illustrated with examples from geometri...

Finding maximum likelihood parameter values for Finite Mixture Model (FMM) is often done with the Expectation Maximization (EM) algorithm. However the choice...

A recent paper of Tuy and Hoai-Phuong published in <i>JOGO</i> (2007) 37:557--569 observes that there are errors in the reformulation of a signomial geometr...

Necessary and sufficient conditions are provided for existence of a simple graph <i>G</i>, and for a simple and connected graph <i>G'</i> with given numbers ...

Upper bounds on the average distance \(\overline{l}\) between pairs of vertices of a connected graph with given order \(n\) and minimum degree `(\delta...

The transmission of a vertex in a connected graph is the sum of all distance from that vertex to the others. It is said to be normalized if divided by <i>n-1...

Variable neighborhood search (VNS) is a metaheuristic, or framework for building heuristics, based upon systematic change of neighborhoods both in a decent ...

Minimum sum-of-squares clustering (MSSC) consists in partitioning a given set of <i>n</i> points into <i>k</i> clusters in order to minimize the sum of squar...

A polygon is said to be <i>simple</i> if the only points of the plane belonging to two of its edges are its vertices. We answer the question of finding, ...

With the help of the Graffiti system, Fajtlowicz conjectured around 1992 that the average distance between two vertices of a connected graph <i>G</i> is at ...

Methods, models, heuristic and exact algorithms for clustering are reviewed from a mathematical programming view point.

A recent proof of NP-hardness of Euclidean sum-of-squares clustering, due to Drineas et al., <i>Machine Learning</i> 56, 9--33, 2004, is not valid. An altern...

Let <img src="/cgi-bin/mimetex.cgi?G=(V,E)"> be a simple, undirected graph of order <img src="/cgi-bin/mimetex.cgi?n"> and size <img src="/cgi-bin/mimetex.cg...

In this note we suggest a simple but efficient modification of the well-known Nelder-Mead (NM) simplex search method for unconstrained optimization. Instead ...

The hexagon and heptagon with unit diameter and maximum sum of Euclidean distances between vertices are determined by enumerating diameter configurations, an...