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.

Keywords

• reachable, reachability matrix, reach eigen values,reach spectrum, reach energy