University of KashanIranian Journal of Mathematical Chemistry2228-648913120220301Maximum Variable Connectivity Index of n-Vertex Trees334411201710.22052/ijmc.2022.243077.1584ENShamailaYousafDepartment of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, PakistanDepartment of Mathematics, University of Gujrat, Gujrat, Pakistan0000-0003-2732-6601Akhlaq AhmadBhattiDepartment 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.pdf