فهرست نشریات علمی دسترسی آزاد ایران

This article explores the adjacency matrix of a two-sided group graph and its properties. We introduce the two-sided color group digraph to generalize the Cayley color graph and the two-sided group digraph. We also obtain the adjacency matrix of the latter digraph and provide a criterion for determining the normality of the adjacency matrix of a two-sided group graph. Moreover, we prove that if all the two-sided group digraphs of valency two for a certain group G are normal, then G is a Hamiltonian group. We also show that if a strongly connected two-sided group digraph of valency two is normal, the corresponding group is isomorphic to the product of two groups: a cyclic group with either Tk,n or Hp,q, or an abelian group.