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Appears in Collections:Computing Science and Mathematics Research Reports
Peer Review Status: Refereed
Title: Spectral Reconstruction and Isomorphism of graphs using variable neighbourhood search
Author(s): Caporossi, Gilles
Cvetkovic, Dragos
Rowlinson, Peter
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Citation: Caporossi G, Cvetkovic D & Rowlinson P (2013) Spectral Reconstruction and Isomorphism of graphs using variable neighbourhood search. Les Cahiers du GERAD, G-2013-73. GERAD.
Keywords: Spectral distance
graph angles
graph isomorphism
variable neighbourhood search
Issue Date: Oct-2013
Date Deposited: 28-Jan-2014
Publisher: GERAD
Series/Report no.: Les Cahiers du GERAD, G-2013-73
Abstract: The Euclidean distance between the eigenvalue sequences of graphs G and H, on the same number of vertices, is called the spectral distance between G and H. This notion is the basis of a heuristic algorithm for reconstructing a graph with prescribed spectrum. By using a graph Γ constructed from cospectral graphs G and H, we can ensure that G and H are isomorphic if and only if the spectral distance between Γ  and G+K2 is zero. This construction is exploited to design a heuristic algorithm for testing graph isomorphism. We present preliminary experimental results obtained by implementing these algorithms in conjunction with a meta-heuristic known as a variable neighbourhood search.
Type: Research Report
Rights: Authors retain copyright.
Affiliation: HEC Montreal
Mathematical Institute SANU

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