Result: Walks and regular integral graphs
Title:
Walks and regular integral graphs
Source:
Special issue devoted to papers presented at the Aveiro Workshop on Graph SpectraLinear algebra and its applications. 423(1):119-135
Publisher Information:
New York, NY: Elsevier Science, 2007.
Publication Year:
2007
Physical Description:
print, 23 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, Borne inférieure, Lower bound, Cota inferior, Comptage, Counting, Contaje, Dénombrement, Enumeration(counting), Recuento, Graphe biparti, Bipartite graph, Grafo bipartido, Graphe régulier, Regular graph, Grafo regular, Problème valeur propre, Eigenvalue problem, Problema valor propio, Régularité, Regularity, Regularidad, Spectre, Spectrum, Espectro, Théorie graphe, Graph theory, Teoría grafo, 05C50;Integral graphs, Bipartite graphs, Graph eigenvalues, Regular graphs
Document Type:
Conference
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
University of Niš, Serbia and Montenegro
Federal University of Rio de Janeiro, Brazil
Federal University of Fluminense, Niteroi, Brazil
Federal University of Rio de Janeiro, Brazil
Federal University of Fluminense, Niteroi, 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.18660521
Database:
PASCAL Archive
Further Information
We establish a useful correspondence between the closed walks in regular graphs and the walks in infinite regular trees, which, after counting the walks of a given length between vertices at a given distance in an infinite regular tree, provides a lower bound on the number of closed walks in regular graphs. This lower bound is then applied to reduce the number of the feasible spectra of the 4-regular bipartite integral graphs by more than a half. Next, we give the details of the exhaustive computer search on all 4-regular bipartite graphs with up to 24 vertices, which yields a total of 47 integral graphs.