Report
Two-geodesic transitive graphs of order $p^n$ with $n\leq3$
| العنوان: | Two-geodesic transitive graphs of order $p^n$ with $n\leq3$ |
|---|---|
| المؤلفون: | Huang, Jun-Jie, Feng, Yan-Quan, Zhou, Jin-Xin, Yin, Fu-Gang |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05C25, 20B25, 05E18 |
| الوصف: | A vertex triple $(u,v,w)$ of a graph is called a $2$-geodesic if $v$ is adjacent to both $u$ and $w$ and $u$ is not adjacent to $w$. A graph is said to be $2$-geodesic transitive if its automorphism group is transitive on the set of $2$-geodesics. In this paper, a complete classification of $2$-geodesic transitive graphs of order $p^n$ is given for each prime $p$ and $n\leq 3$. It turns out that all such graphs consist of three small graphs: the complete bipartite graph $K_{4,4}$ of order $8$, the Schl\"{a}fli graph of order $27$ and its complement, and fourteen infinite families: the cycles $C_p, C_{p^2}$ and $C_{p^3}$, the complete graphs $K_p, K_{p^2}$ and $K_{p^3}$, the complete multipartite graphs $K_{p[p]}$, $K_{p[p^2]}$ and $K_{p^2[p]}$, the Hamming graph $H(2,p)$ and its complement, the Hamming graph $H(3,p)$, and two infinite families of normal Cayley graphs on extraspecial group of order $p^3$ and exponent $p$. Comment: 27 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2207.10919 |
| رقم الانضمام: | edsarx.2207.10919 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |