University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 13 1 2022 03 01 Maximum Variable Connectivity Index of n-Vertex Trees 33 44 112017 10.22052/ijmc.2022.243077.1584 EN Shamaila Yousaf Department 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, Pakistan Akhlaq Ahmad Bhatti Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, Pakistan Journal Article 2021 09 05 In 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 ∑v1v2∈E(G) ((dv1 + θ*)(dv2 + θ*))−1/2, where θ* is a non-negative real number and dv1 is the degree of vertex V1 in G. The main objective of the present study is to prove the conjecture proposed in [19]. In this study, we will show that the Pn (path graph) has the maximum variable connectivity index among the collection of trees whose order is n, where n ≥ 4.

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