Semisymmetric Cubic Graphs of Order $10p^2$

Abstract

A regular graph $\mathrm{\Gamma }$ is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. Some authors classified semisymmetric cubic graphs of orders $10p$ and $10p^2$. Also, it is proved that there is no connected semisymmetric cubic graph of order $10p^3$. In this paper, we continue this work and prove that there is no connected semisymmetric cubic graph of order $10p^n$, where $n\ge 4$, $p\ge 7$, and $p\ne 11$.