%0 Journal Article
%T Maximum Variable Connectivity Index of n-Vertex Trees
%J Iranian Journal of Mathematical Chemistry
%I University of Kashan
%Z 2228-6489
%A Yousaf, Shamaila
%A Bhatti, Akhlaq Ahmad
%D 2022
%\ 03/01/2022
%V 13
%N 1
%P 33-44
%! Maximum Variable Connectivity Index of n-Vertex Trees
%K Chemical graph theory
%K Variable connectivity index
%K Variable Randić index
%K Trees
%K extremal problem
%R 10.22052/ijmc.2022.243077.1584
%X 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.
%U https://ijmc.kashanu.ac.ir/article_112017_f07c10b0c724a415f616bbe93237be3c.pdf