Pierre Hansen
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Spectral properties of threshold graphs
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...
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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 \(n\)
....
Distributed integral column generation
The Integral Simplex Using Decomposition (ISUD) algorithm has been developed recently to solve large set partitioning problems (SPPs) in a primal way, i.e.,...
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Clustering is the subject of active research in several fields such as operations research, statistics, pattern recognition, and machine learning. The range ...
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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...
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Let \({\mathcal D(G)}\)
, \({\mathcal D}^L(G)={\mathcal Diag(Tr)} - {\mathcal D(G)}\)
and \({\mathcal D}^Q(G)={\mathcal Diag(Tr)} + {\mathcal D(G)}\)
b...
Let \(G\)
be a graph of order \(n\)
. The energy \(\mathcal{E}(G)\)
of a simple graph \(G\)
is the sum of
absolute values of the eigenvalues of its ...
Given an integer solution, the integral simplex using decomposition (ISUD) seeks a descent direction that leads to an improved adjacent integer solution. It ...
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Necessary and sufficient conditions are provided for the existence of a simple
graph, or a simple connected graph with given
numbers \(m_{ij}\)
of edges ...
The distance, distance Laplacian and distance signless Laplacian spectra of a connected graph \(G\)
are the spectra of the distance, distance Laplacian and...
On the nullity number of graphs
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 ...
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Graph theoretical heuristics are used extensively in many fields to solve approximately large scale optimization problems. Graph theoretical heuristics can a...
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In the present paper we are interested in the study of the distance Laplacian eigenvalues of a connected graph with fixed order \(n\)
and chromatic number ...
The geometric-arithmetic index \(GA\)
of a graph \(G\)
is the sum of ratios, over all edges of \(G\)
, of the geometric mean to the arithmetic mean of t...
In the present paper, we prove lower and upper bounds for each of the ratios \(GA/\delta\)
, \(GA/\overline{d}\)
and \(\Delta\)
, in terms of the order `...
In the present paper, we compare the geometric-arithmetic index \(GA\)
and the chromatic number \(\chi\)
of a connected graph with given order. We prove,...
Variable neighborhood search (VNS) is a framework for building heuristics, based upon systematic changes of neighborhoods both in a descent phase, to find a...
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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...
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