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Finite $s$-geodesic transitive graphs under certain girths
Jun-Jie Huang
https://arxiv.org/abs/2506.05803 https://arxiv.org/pdf/2506.…

Finite $s$-geodesic transitive graphs under certain girths
For an integer $s\geq1$ and a graph $Γ$, a path $(u_0, u_1, \ldots, u_{s})$ of vertices of $Γ$ is called an {\em $s$-geodesic} if it is a shortest path from $u_0$ to $u_{s}$. We say that $Γ$ is {\em $s$-geodesic transitive} if, for each $i\leq s$, $Γ$ has at least one $i$-geodesic, and its automorphism group is transitive on the set of $i$-geodesics. In 2021, Jin and Praeger [J. Combin. Theory Ser. A 178 (2021) 105349] have studied $3$-geodesic transitive graphs of girth $5$ or $6$, and the…

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Sagt drüben gerne bescheid, dass wir nun…