Two-geodesic transitive graphs of prime power order

Jin, W.

Two-geodesic transitive graphs of prime power order

Document Type : Research Paper

Author

W. Jin ¹^{, 2}

¹ School of Statistics‎, ‎Jiangxi University of Finance and Economics‎, ‎Nanchang‎, ‎Jiangxi‎, ‎330013‎, ‎P.R‎. ‎China

² Research Center of Applied Statistics‎, ‎Jiangxi University of Finance and Economics‎, ‎Nanchang‎, ‎Jiangxi‎, ‎330013‎, ‎P.R‎. ‎China.

Abstract

In a non-complete graph $\Gamma$, a vertex triple $(u,v,w)$ with $v$ adjacent to both $u$ and $w$ is called a $2$-geodesic if $uneq w$ and $u,w$ are not adjacent. The graph $\Gamma$ is said to be $2$-geodesic transitive if its automorphism group is transitive on arcs, and also on 2-geodesics. We first produce a reduction theorem for the family of $2$-geodesic transitive graphs of prime power order. Next, we classify such graphs which are also vertex quasiprimitive.

Keywords

Main Subjects

05-XX Combinatorics

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