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Smith forms for adjacency matrices of circulant graphs

Williams, Gerald (2014) 'Smith forms for adjacency matrices of circulant graphs.' Linear Algebra and its Applications, 443. pp. 21-33. ISSN 0024-3795

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Abstract

We calculate the Smith normal form of the adjacency matrix of each of the following graphs or their complements (or both): complete graph, cycle graph, square of the cycle, power graph of the cycle, distance matrix graph of cycle, Andrásfai graph, Doob graph, cocktail party graph, crown graph, prism graph, Möbius ladder. The proofs operate by finding the abelianization of a cyclically presented group whose relation matrix is column equivalent to the required adjacency matrix.

Item Type: Article
Uncontrolled Keywords: Smith normal form; Circulant graph; Adjacency matrix
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 07 Jan 2014 11:32
Last Modified: 06 Jan 2022 13:26
URI: http://repository.essex.ac.uk/id/eprint/8578

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