Semisymmetric Cubic Graphs of Order \(10p^2\)

Abstract

A regular graph \(\Gamma\) 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 \(n \geq 4\), \(p \geq 7\), and \(p \neq 11\).