Generalized Randić Estrada Indices of Graphs

Eber Lenes (), Exequiel Mallea-Zepeda, Luis Medina and Jonnathan Rodríguez
Additional contact information
Eber Lenes: Área de Ciencias Básicas Exactas, Grupo de Investigación Deartica, Universidad del Sinú, Cartagena 130001, Colombia
Exequiel Mallea-Zepeda: Departamento de Matemática, Universidad de Tarapacá, Arica 1000000, Chile
Luis Medina: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Av. Angamos 601, Antofagasta 1240000, Chile
Jonnathan Rodríguez: Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Av. Angamos 601, Antofagasta 1240000, Chile

Mathematics, 2022, vol. 10, issue 16, 1-14

Abstract: Let G be a simple undirected graph on n vertices. V. Nikiforov studied hybrids of A G and D G and defined the matrix A α G for every real α ∈ [ 0 , 1 ] as A α G = α D G + ( 1 − α ) A G . In this paper, we define the generalized Randić matrix for graph G , and we introduce and establish bounds for the Estrada index of this new matrix. Furthermore, we find the smallest value of α for which the generalized Randić matrix is positive semidefinite. Finally, we present the solution to the problem proposed by V. Nikiforov. The problem consists of the following: for a given simple undirected graph G , determine the smallest value of α for which A α G is positive semidefinite.

Keywords: convex combination of matrices; generalized Randi? matrix; Estrada index; positive semidefinite matrix; bipartite graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/16/2932/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/16/2932/ (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:10:y:2022:i:16:p:2932-:d:888105

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 ().