Smallest graphs with given generalized quaternion automorphism group

For n≥3, a smallest graph whose automorphism group is isomorphic to the generalized quaternion group is constructed. If n≠3, then such a graph has 2n+1 vertices and 2n+2 edges. In the special case when n=3, a smallest graph has 16 vertices but 44 edges.

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Bibliographic Details
Published inJournal of graph theory Vol. 87; no. 4; pp. 430 - 442
Main Authors Graves, Christina, Graves, Stephen J., Lauderdale, L.‐K.
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.04.2018
Subjects
automorphism groups of graphs
Automorphisms
Graph theory
quaternion group
Quaternions
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Summary:For n≥3, a smallest graph whose automorphism group is isomorphic to the generalized quaternion group is constructed. If n≠3, then such a graph has 2n+1 vertices and 2n+2 edges. In the special case when n=3, a smallest graph has 16 vertices but 44 edges.
ISSN:0364-9024
1097-0118
DOI:10.1002/jgt.22166