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Smallest graphs with given generalized quaternion automorphism group

Publisher： John Wiley & Sons Inc

E-ISSN： 1097-0118|87|4|430-442

ISSN： 0364-9024

Source： JOURNAL OF GRAPH THEORY, Vol.87, Iss.4, 2018-04, pp. : 430-442

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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Abstract

AbstractFor $n \geq 3$ , a smallest graph whose automorphism group is isomorphic to the generalized quaternion group is constructed. If $n \neq 3$ , then such a graph has $2^{n + 1}$ vertices and $2^{n + 2}$ edges. In the special case when $n = 3$ , a smallest graph has 16 vertices but 44 edges.

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