Reach Energy of Digraphs

Abstract

A Digraph D consists of two finite sets ), where  denotes the vertex set and denotes the arc set. For vertices  if there exists a directed path from  to  then  is said to be reachable from  and vice versa. The Reachability matrix of D is the  matrix , where  if  is reachable from and  otherwise. The eigen values corresponding to the reachability matrix are called reach eigen values. The reach energy of a digraph is defined by where  is the eigen value of the reachability matrix. In this paper we introduce the reach spectrum of a digraph and study its properties and bounds. Moreover, we compute reachspectrum for some digraphs.