On Bond Incident Degree Indices of Fixed-Size Bicyclic Graphs with Given Matching Number

Akbar Ali (), Abeer M. Albalahi, Abdulaziz M. Alanazi, Akhlaq A. Bhatti, Tariq Alraqad, Hicham Saber and Adel A. Attiya
Additional contact information
Akbar Ali: Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia
Abeer M. Albalahi: Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia
Abdulaziz M. Alanazi: Department of Mathematics, Faculty of Sciences, University of Tabuk, Tabuk P.O. Box 741, Saudi Arabia
Akhlaq A. Bhatti: Department of Sciences and Humanities, National University of Computer and Emerging Sciences, B-Block, Faisal Town, Lahore 54770, Pakistan
Tariq Alraqad: Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia
Hicham Saber: Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia
Adel A. Attiya: Department of Mathematics, College of Science, University of Ha’il, Ha’il 81451, Saudi Arabia

Mathematics, 2024, vol. 12, issue 23, 1-14

Abstract: A connected graph with p vertices and q edges satisfying q = p + 1 is referred to as a bicyclic graph. This paper is concerned with an optimal study of the BID (bond incident degree) indices of fixed-size bicyclic graphs with a given matching number. Here, a BID index of a graph G is the number BID f ( G ) = ∑ v w ∈ E ( G ) f ( d G ( v ) , d G ( w ) ) , where E ( G ) represents G ’s edge set, d G ( v ) denotes vertex v ’s degree, and f is a real-valued symmetric function defined on the Cartesian square of the set of all different members of G ’s degree sequence. Our results cover several existing indices, including the Sombor index and symmetric division deg index.

Keywords: bond incident degree index; topological index; bicyclic graph; matching number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/23/3806/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/23/3806/ (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:12:y:2024:i:23:p:3806-:d:1534453

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 ().