Samira Fallahpour - Faculty of Mathematical and Computer Science, kharazmi university, Tehran, Iran
Mohammadreza Salarian - Faculty of Mathematical and Computer Science, kharazmi university, Tehran, Iran

A simple graph is called semisymmetric if it is regular and edge-transitive but not vertex-transitive. Let p be an arbitrary prime. Folkman [J. Folkman, Regular line-symmetric graphs, J. Combinatorial Theory, \textbf{۳} (۱۹۶۷) ۲۱۵--۲۳۲.] proved that there are no cubic semisymmetric graphs of order ۲p or ۲p^{۲}. In this paper, an extension of his result in the case of cubic graphs of order ۴۴p or ۴۴p^{۲} is given. By using group theoretic methods, we prove that there are no connected cubic semisymmetric graphs of order ۴۴p or ۴۴p^{۲}.

semisymmetric graph, edge-transitive graph, vertex-transitive graph