A comprehensive study on fuzzy and crisp graph indices: generalized formulae, proximity and accuracy analysis-Reference-Cited by-同舟云学术

A comprehensive study on fuzzy and crisp graph indices: generalized formulae, proximity and accuracy analysis

Published:2023 Issue:12 Volume:8 Page:30922-30939
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Mirza Muhammad Umar¹,Anjum Rukhshanda¹,Youssef Maged Z.²,Alsuraiheed Turki³

Affiliation:

1. Department of Mathematics and Statistics, University of Lahore, Lahore, Pakistan

2. Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University(IMSIU), Riyadh, Saudi Arabia

3. Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia

Abstract

<abstract><p>This article presents a set of generalized $ \wp $-dependent formulae for fuzzy and crisp versions of various graph indices, including the first and second Zagreb indices, harmonic index and Randic index. These formulae are applied to the identity graph of the commutative ring $ Z_{\wp} $, and the resulting indices are calculated by using MATLAB software for 20 prime numbers. The generated data were applied for machine learning by using Python and Jupyter notebook to investigate the relationship between fuzzy and crisp indices. The article also includes the relationship between fuzzy and crisp indices in the form of six-degree polynomials and an error analysis.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference36 articles.

1. H. Bielak, K. Broniszewska, Eccentric distance sum index for some classes of connected graphs, Ann. Uni. Mariae Curie-Sklodowska, Sec. A Math., 71 (2017), 25–32. https://doi.org/10.17951/a.2017.71.2.25

2. M. Mogharrab, Eccentric connectivity index of bridge graphs, Optoelectron. Adv. Mater. Commun., 4 (2010), 1866–1867.

3. N. De, On eccentric connectivity index and polynomial of thorn graph, Sci. Res., 3 (2012), 21477. https://doi.org/10.4236/am.2012.38139

4. R. Rasi, S. M. Sheikholeslami, A. Behmaram, An upper bound on the first Zagreb index in trees, Iran. J. Math. Chem., 8 (2017), 71–82. https://doi.org/10.22052/ijmc.2017.42995

5. X. Geng, S. Li, M. Zhang, Extremal values on the eccentric distance sum of trees, Dis. Appl. Math., 161 (2013), 2427–2439. https://doi.org/10.1016/j.dam.2013.05.023

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Machine Learning Driven Exploration of Energies and Generalization of Topological Indices for the Fuzzy Conjugate Graph of Dihedral Group;IEEE Access;2024