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On the Automorphism Groups of Almost All Circulant Graphs and Digraphs

We attempt to determine the structure of the automorphism group of a generic circulant graph. We first show that almost all circulant graphs have automorphism groups as small as possible. Dobson has conjectured that almost all of the remaining circulant (di)graphs (those whose automorphism groups are not as small as possible) are normal circulant (di)graphs. We show this conjecture is not true in general, but is true if we consider only those circulant (di)graphs whose orders are in a “large” subset of integers. We note that all non-normal circulant (di)graphs can be classified into two natural classes (generalized wreath products, and deleted wreath type), and show that neither of these classes contains almost every non-normal circulant digraph.

Identiferoai:union.ndltd.org:MSSTATE/oai:scholarsjunction.msstate.edu:td-4362
Date17 August 2013
CreatorsBhoumik, Soumya
PublisherScholars Junction
Source SetsMississippi State University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceTheses and Dissertations

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