Reach Energy of Digraphs

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 val...

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Bibliographic Details
Published inRatio mathematica Vol. 44; pp. 363 - 370
Main Authors Mahalakshmi, V, B Vijaya Praba, Palani, K
Format Journal Article
LanguageEnglish
Published Pescara Accademia Piceno Aprutina dei Velati in Teramo (APAV) 01.12.2022
Accademia Piceno Aprutina dei Velati
Subjects
Apexes
Eigenvalues
Energy
Graph theory
Mathematics
reachable, reachability matrix, reach eigen values,reach spectrum, reach energy
Vertex sets
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Summary: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.
ISSN:1592-7415
2282-8214
DOI:10.23755/rm.v44i0.926