Reach Energy of Digraphs

Authors

  • V Mahalakshmi Assistant Professor , PG & Research Department of Mathematics, A.P.C. Mahalaxmi College for Women Thoothukudi, India
  • B Vijaya Praba Research Scholar Reg.No: 21212012092002 (PG & Research Department of Mathematics, A.P.C. Mahalaxmi College for Women Thoothukudi, India
  • K Palani PG & Research Department of Mathematics, A.P.C. Mahalaxmi College for Women Thoothukudi, India

DOI:

https://doi.org/10.23755/rm.v44i0.926

Keywords:

Reachable, Reachability matrix, reach eigen values, reach spectrum, Reach energy

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.

References

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Published

2022-12-11

Issue

Vol. 44 (2022): Special Issue: Recent Trends in Mathematics and its Applications

Section

Volume 45-2023

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