Sharp Bounds for the General Randić Index of R-Graph Products

Xiujun Zhang; Muhammad Aamer Rashid; Sarfraz Ahmad; Muhammad Imran; Shehnaz Akhter; Muhammad Kamran Siddiqui

doi:10.61091/ars159-05

Sharp Bounds for the General Randić Index of R-Graph Products

Xiujun Zhang, Muhammad Aamer Rashid, Sarfraz Ahmad, Muhammad Imran, Shehnaz Akhter, Muhammad Kamran Siddiqui

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

A chemical structure specifies the molecular geometry of a given molecule or solid in the form of atom arrangements. A way to analyze its properties is to stimulate its formation as, product of two or more simpler graphs. In this article, we take this idea to find upper and lower bounds for the generalized Randić index R_α of four types of graph products, by using combinatorial inequalities. We finish this paper providing the bounds for R_α of a line graph and rooted product of graphs.

Original language	English
Pages (from-to)	41-50
Number of pages	10
Journal	Ars Combinatoria
Volume	159
DOIs	https://doi.org/10.61091/ars159-05
Publication status	Published - 2024

Keywords

corona product
line graph
R-graphs
rooted product
The general Randić index

ASJC Scopus subject areas

General Mathematics

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10.61091/ars159-05

Cite this

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abstract = "A chemical structure specifies the molecular geometry of a given molecule or solid in the form of atom arrangements. A way to analyze its properties is to stimulate its formation as, product of two or more simpler graphs. In this article, we take this idea to find upper and lower bounds for the generalized Randi{\'c} index Rα of four types of graph products, by using combinatorial inequalities. We finish this paper providing the bounds for Rα of a line graph and rooted product of graphs.",

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author = "Xiujun Zhang and Rashid, {Muhammad Aamer} and Sarfraz Ahmad and Muhammad Imran and Shehnaz Akhter and Siddiqui, {Muhammad Kamran}",

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doi = "10.61091/ars159-05",

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AU - Rashid, Muhammad Aamer

AU - Ahmad, Sarfraz

AU - Imran, Muhammad

AU - Akhter, Shehnaz

AU - Siddiqui, Muhammad Kamran

PY - 2024

Y1 - 2024

N2 - A chemical structure specifies the molecular geometry of a given molecule or solid in the form of atom arrangements. A way to analyze its properties is to stimulate its formation as, product of two or more simpler graphs. In this article, we take this idea to find upper and lower bounds for the generalized Randić index Rα of four types of graph products, by using combinatorial inequalities. We finish this paper providing the bounds for Rα of a line graph and rooted product of graphs.

AB - A chemical structure specifies the molecular geometry of a given molecule or solid in the form of atom arrangements. A way to analyze its properties is to stimulate its formation as, product of two or more simpler graphs. In this article, we take this idea to find upper and lower bounds for the generalized Randić index Rα of four types of graph products, by using combinatorial inequalities. We finish this paper providing the bounds for Rα of a line graph and rooted product of graphs.

KW - corona product

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KW - R-graphs

KW - rooted product

KW - The general Randić index

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JF - Ars Combinatoria

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Sharp Bounds for the General Randić Index of R-Graph Products

Abstract

Keywords

ASJC Scopus subject areas

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