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
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
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
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.