University of KashanIranian Journal of Mathematical Chemistry2228-648913120220301The Schultz Index for Product Graphs11711199610.22052/ijmc.2022.243309.1597ENJhon JaneAguilar-AlarconFacultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas
s/n, Col. La Haciendita. Chilpancingo, Guerrero, MéxicoGerardo Reyna-HernandezFacultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas
s/n, Col. La Haciendita. Chilpancingo, Guerrero, MéxicoJesus Romero-ValenciaFacultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas
s/n, Col. La Haciendita. Chilpancingo, Guerrero, México0000-0002-3606-890XOmar Rosario-CayetanoFacultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas
s/n, Col. La Haciendita. Chilpancingo, Guerrero, MéxicoJournal Article20211124Among the binary operations made with graphs, the cartesian, corona, and lexicographic are three well-known products, as well as the cartesian sum. Topological indices are graph invariants used to describe graphs associated with molecules, one of these is the Schultz index, which can be obtained as ∑ <sub>u≠v</sub> (deg u+ deg v) d(u,v), where the sum runs over all pairs of distinct vertices of the graph. In this paper, we give explicit expressions for the Schultz index of cartesian and corona, with alternative proofs to those given in the literature, as well as for lexicographic product and the cartesian sum, all of these formulas involve order and size of factors, additionally, the first three involve both Wiener and Schultz indices of factors, corona and lexicographic also involve Zagreb index and the last one just Zagreb. https://ijmc.kashanu.ac.ir/article_111996_04c009800fe7249f4840b5eccec457dd.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648913120220301On the Difference of Atom-Bond Connectivity Index and Randić Index with Some Topological Indices193211201610.22052/ijmc.2022.246069.1611ENRoslan HasniSpecial Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean
Engineering Technology and Informatics, University Malaysia Terengganu, 21030 UMT Kuala
Nerus,Terengganu, Malaysia0000-0003-3695-2145Mohamad Nazri HusinSpecial Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean
Engineering Technology and Informatics, University Malaysia Terengganu, 21030 UMT Kuala
Nerus,Terengganu, MalaysiaFateme MovahediDepartment of Mathematics, Faculty of Science, Golestan University, Gorgan, Iran0000-0001-7863-7915Rudrusamy GobithaasanSpecial Interest Group on Modelling and Data Analytics (SIGMDA), Faculty of Ocean
Engineering Technology and Informatics, University Malaysia Terengganu, 21030 UMT Kuala
Nerus,Terengganu, MalaysiaMohammad Hadi AkhbariDepartment of Mathematics, Estahban Branch, Islamic Azad University, Estahban, IranJournal Article20220222Assume denotes a connected and simple graph with edge set <em>E</em>(<em>G</em>) as well as vertex set <em>V</em>(<em>G</em>). In chemical graph theory, the atom-bond connectivity index, as well as the Randić index of graph are two well-defined topological indices. In addition, Ali and Du [On the difference between <em> ABC </em>and Randić indices of binary and chemical trees, <em>Int. J. Quantum Chem.</em> (2017) e25446] recently unveiled the distinction between Randić and <em>ABC</em> indices. In this report, we study the link between the difference of Randić and <em>ABC</em> indices with certain well-studied topological indices. https://ijmc.kashanu.ac.ir/article_112016_6e601265b209c1d8a83ff1f0e4fd48cb.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648913120220301Maximum Variable Connectivity Index of n-Vertex Trees334411201710.22052/ijmc.2022.243077.1584ENShamaila YousafDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, Pakistan
Department of Mathematics, University of Gujrat, Gujrat, Pakistan0000-0003-2732-6601Akhlaq Ahmad BhattiDepartment of Sciences and Humanities,
National University of Computer and Emerging Sciences, Lahore Campus,
B-Block, Faisal Town, Lahore, PakistanJournal Article20210905In QSAR and QSPR studies the most commonly used topological index was proposed by chemist Milan Randić in 1975 called Randić branching index or path-one molecular connectivity index, 1χ and it has many applications. In the extension of connectivity indices, in early 1990s, chemist Milan Randic´ introduced variable Randić index deﬁned as ∑<sub>v1v2∈E(G)</sub> ((d<sub>v1</sub> + θ*)(d<sub>v2</sub> + θ*))<sup>−1/2</sup>, where θ* is a non-negative real number and d<sub>v1</sub> is the degree of vertex V<sub>1</sub> in <em>G</em>. The main objective of the present study is to prove the conjecture proposed in [19]. In this study, we will show that the <em>P<sub>n</sub></em> (path graph) has the maximum variable connectivity index among the collection of trees whose order is <em>n</em>, where <em>n</em> ≥ 4.https://ijmc.kashanu.ac.ir/article_112017_f07c10b0c724a415f616bbe93237be3c.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648913120220501On the Graovc-Ghorbani and Atom-Bond Connectivity Indices of Graphs from Primary Subgraphs457211203210.22052/ijmc.2022.246079.1612ENNima GhanbariDepartment of Informatics , University of Bergen, P.O. Box 7803, 5020 Bergen, Norway0000-0001-5063-3461Journal Article20220223Let G=(V,E) be a finite simple graph. The Graovac-Ghorbani index of a graph G is defined as ABC<sub>GG</sub>(G)=∑<sub>uv∈E(G)</sub> √((n<sub>u</sub>(uv,G)+n<sub>v</sub>(uv,G)-2)/(n<sub>u</sub>(uv,G)n<sub>v</sub>(uv,G))), where n<sub>u</sub>(uv,G) is the number of vertices closer to vertex u than vertex v of the edge uv∈E(G). n<sub>v</sub>(uv,G) is defined analogously. The atom-bond connectivity index of a graph G is defined as ABC(G)=∑<sub>uv∈E(G)</sub>√((d<sub>u</sub>+d<sub>v</sub>-2)(d<sub>u</sub>dv)), where d<sub>u</sub> is the degree of vertex u in G. Let G be a connected graph constructed from pairwise disjoint connected graphs G<sub>1</sub>,...,G<sub>k</sub> by selecting a vertex of G<sub>1</sub>, a vertex of G<sub>2</sub>, and identifying these two vertices. Then continue in this manner inductively. We say that G is obtained by point-attaching from G<sub>1</sub>,...,G<sub>k</sub> and that G<sub>i</sub> 's are the primary subgraphs of G. In this paper, we give some lower and upper bounds on Graovac-Ghorbani and atom-bond connectivity indices for these graphs. Additionally, we consider some particular cases of these graphs that are of importance in chemistry and study their Graovac-Ghorbani and atom-bond connectivity indices.https://ijmc.kashanu.ac.ir/article_112032_5a6df578363ac2633f07b1ea288215d1.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-648913120220330QSPR Analysis of Some Novel Extension and Generalization of Sombor Index738411203310.22052/ijmc.2022.246111.1613ENAnkur BharaliDepartment of Mathematics, Dibrugarh university, India-7860040000-0001-8642-3933Jibonjyoti BuragohainDepartment of Mathematics, Pragjyotish College, India-781009Amitav DoleyDepartmrnt of Mathematics, DSHK College, India-786001Journal Article20220228Although many indices are strongly correlated with various chemical as well as physical properties of a molecular compound but some of them lack proper geometrical interpretations. A newly introduced index called Sombor index is able to catch the attention of the researchers because of its connection with the notion of “2-norm”. In this paper, we propose the status version of the Sombor index. Further, we discuss a generalization of our proposed index and carry out QSPR analysis. Some mathematical properties of the generalization are also discussed.https://ijmc.kashanu.ac.ir/article_112033_5f4b9f127c374ea3bffdfd2960f69a05.pdf