A Note on the Estrada Index of the A ? -Matrix

Jonnathan Rodríguez and Hans Nina
Additional contact information
Jonnathan Rodríguez: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Av. Angamos 601, Antofagasta 1240000, Chile
Hans Nina: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Av. Angamos 601, Antofagasta 1240000, Chile

Mathematics, 2021, vol. 9, issue 8, 1-7

Abstract: Let G be a graph on n vertices. The Estrada index of G is an invariant that is calculated from the eigenvalues of the adjacency matrix of a graph. V. Nikiforov studied hybrids of A ( G ) and D ( G ) and defined the A ? -matrix for every real ? ? [ 0 , 1 ] as: A ? ( G ) = ? D ( G ) + ( 1 ? ? ) A ( G ) . In this paper, using a different demonstration technique, we present a way to compare the Estrada index of the A ? -matrix with the Estrada index of the adjacency matrix of the graph G . Furthermore, lower bounds for the Estrada index are established.

Keywords: Estrada index; ?-adjacency matrix; adjacency matrix; Laplacian matrix (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/8/811/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/8/811/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:8:p:811-:d:532285

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().