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FINITE 3-GEODESIC TRANSITIVE BUT NOT 3-ARC TRANSITIVE GRAPHS

Part of: Algebraic combinatorics Permutation groups

Published online by Cambridge University Press:  23 September 2014

WEI JIN
WEI JIN*
Affiliation:
School of Statistics, Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 330013, PR China email jinwei@jxufe.edu.cn
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Abstract

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In this paper, we first prove that for $g\in \{3,4\}$, there are infinitely many 3-geodesic transitive but not 3-arc transitive graphs of girth $g$ with arbitrarily large diameter and valency. Then we classify the family of 3-geodesic transitive but not 3-arc transitive graphs of valency 3 and those of valency 4 and girth 4.

Keywords

3-geodesic transitive graph3-arc transitive graphautomorphism group

MSC classification

Primary: 05E18: Group actions on combinatorial structures
Secondary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 2 , April 2015 , pp. 183 - 190
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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