On the Line Graph Associated to the Total Graph of a Module

Abstract

Let R be a commutative ring with  unity  and  M  be an R-module  with T Γ(M ) be its total  graph.   The  subject  of this  article  is the  investigation of the  properties  of the  corresponding  line graph  L(T Γ(M )).In  particular, we determine  the  girth  and clique number  of L(T Γ(M )).  In addition  to that, we find a condition  for L(T Γ(M )) to be Eulerian.