Result: Old and new results on algebraic connectivity of graphs
Title:
Old and new results on algebraic connectivity of graphs
Authors:
Source:
Special issue devoted to papers presented at the Aveiro Workshop on Graph SpectraLinear algebra and its applications. 423(1):53-73
Publisher Information:
New York, NY: Elsevier Science, 2007.
Publication Year:
2007
Physical Description:
print, 74 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Théorie des graphes, Graph theory, Algèbre, Algebra, Algèbre linéaire et multilinéaire, matrices, Linear and multilinear algebra, matrix theory, Invariant, Invariante, Laplacien, Laplacian, Laplaciano, Optimisation combinatoire, Combinatorial optimization, Optimización combinatoria, Problème combinatoire, Combinatorial problem, Problema combinatorio, Problème valeur propre, Eigenvalue problem, Problema valor propio, Spectre, Spectrum, Espectro, Théorie graphe, Graph theory, Teoría grafo, Vecteur propre, Eigenvector, Vector propio, 05C50;Laplacian of graph, Algebraic connectivity, Bounds for the algebraic connectivity, Extremal graphs, Fiedler vectors, Laplacian integral graphs, Limit points, Vertex and edge connectivities
Document Type:
Conference
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Federal University of Rio de Janeiro, Rua João Lira, 106/401 Leblon, Rio de Janeiro 22430-210, Brazil
ISSN:
0024-3795
Rights:
Copyright 2007 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.18660516
Database:
PASCAL Archive
Further Information
This paper is a survey of the second smallest eigenvalue of the Laplacian of a graph G, best-known as the algebraic connectivity of G, denoted a(G). Emphasis is given on classifications of bounds to algebraic connectivity as a function of other graph invariants, as well as the applications of Fiedler vectors (eigenvectors related to a(G)) on trees, on hard problems in graphs and also on the combinatorial optimization problems. Besides, limit points to a(G) and characterizations of extremal graphs to a(G) are described, especially those for which the algebraic connectivity is equal to the vertex connectivity.