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

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

A connected graph with <i>p</i> vertices and <i>q</i> edges satisfying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>=</mo><mi>p</mi...

Full description

Saved in:
Bibliographic Details
Main Authors: Akbar Ali, Abeer M. Albalahi, Abdulaziz M. Alanazi, Akhlaq A. Bhatti, Tariq Alraqad, Hicham Saber, Adel A. Attiya
Format: Article
Language:English
Published: MDPI AG 2024-12-01
Series:Mathematics
Subjects:
bond incident degree index
topological index
bicyclic graph
matching number
Online Access:https://www.mdpi.com/2227-7390/12/23/3806
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A connected graph with <i>p</i> vertices and <i>q</i> edges satisfying <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>=</mo><mi>p</mi><mo>+</mo><mn>1</mn></mrow></semantics></math></inline-formula> 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 <i>G</i> is the number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">BID</mi><mi mathvariant="fraktur">f</mi></msub><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><msub><mo>∑</mo><mrow><mi>v</mi><mi>w</mi><mo>∈</mo><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></msub><mi mathvariant="fraktur">f</mi><mrow><mo>(</mo><msub><mi>d</mi><mi>G</mi></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow><mo>,</mo><msub><mi>d</mi><mi>G</mi></msub><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></semantics></math></inline-formula> represents <i>G</i>’s edge set, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>d</mi><mi>G</mi></msub><mrow><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> denotes vertex <i>v</i>’s degree, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="fraktur">f</mi></semantics></math></inline-formula> is a real-valued symmetric function defined on the Cartesian square of the set of all different members of <i>G</i>’s degree sequence. Our results cover several existing indices, including the Sombor index and symmetric division deg index.
ISSN:2227-7390

Similar Items