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Large circulant graphs of fixed diameter and arbitrary degree

Bevan, David; Erskine, Grahame and Lewis, Robert (2017). Large circulant graphs of fixed diameter and arbitrary degree. Ars Mathematica Contemporanea, 13(2) pp. 275–291.

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Abstract

We consider the degree-diameter problem for undirected and directed circulant graphs. To date, attempts to generate families of large circulant graphs of arbitrary degree for a given diameter have concentrated mainly on the diameter 2 case. We present a direct product construction yielding improved bounds for small diameters and introduce a new general technique for “stitching” together circulant graphs which enables us to improve the current best known asymptotic orders for every diameter. As an application, we use our constructions in the directed case to obtain upper bounds on the minimum size of a subset A of a cyclic group of order n such that the k-fold sumset kA is equal to the whole group. We also present a revised table of largest known circulant graphs of small degree and diameter.

Item Type: Journal Item
Copyright Holders: 2017 The Authors
ISSN: 1855-3974
Keywords: degree-diameter problem; Cayley graphs; circulant graphs; sumsets
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 48897
Depositing User: Grahame Erskine
Date Deposited: 13 Mar 2017 10:48
Last Modified: 16 May 2017 00:41
URI: http://oro.open.ac.uk/id/eprint/48897
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