On the variable inverse sum deg index
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Published:2023
Issue:5
Volume:20
Page:8800-8813
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ISSN:1551-0018
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Container-title:Mathematical Biosciences and Engineering
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language:
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Short-container-title:MBE
Author:
Molina Edil D.1, Bosch Paul2, Sigarreta José M.1, Tourís Eva3
Affiliation:
1. Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No.54 Col. Garita, 39650 Acalpulco Gro., Mexico 2. Facultad de Ingeniería, Universidad del Desarrollo, Ave. La Plaza 680, San Carlos de Apoquindo, Las Condes, Santiago, Chile 3. Departamento de Matemáticas, Universidad Autónoma de Madrid, Campus de Cantoblanco, Madrid 28049, Spain
Abstract
<abstract><p>Several important topological indices studied in mathematical chemistry are expressed in the following way $ \sum_{uv \in E(G)} F(d_u, d_v) $, where $ F $ is a two variable function that satisfies the condition $ F(x, y) = F(y, x) $, $ uv $ denotes an edge of the graph $ G $ and $ d_u $ is the degree of the vertex $ u $. Among them, the variable inverse sum deg index $ IS\!D_a $, with $ F(d_u, d_v) = 1/(d_u^a+d_v^a) $, was found to have several applications. In this paper, we solve some problems posed by Vukičević <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>, and we characterize graphs with maximum and minimum values of the $ IS\!D_a $ index, for $ a < 0 $, in the following sets of graphs with $ n $ vertices: graphs with fixed minimum degree, connected graphs with fixed minimum degree, graphs with fixed maximum degree, and connected graphs with fixed maximum degree. Also, we performed a QSPR analysis to test the predictive power of this index for some physicochemical properties of polyaromatic hydrocarbons.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Computational Mathematics,General Agricultural and Biological Sciences,Modeling and Simulation,General Medicine
Reference34 articles.
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