Maximum Variable Connectivity Index of n-Vertex Trees
نویسندگان
1 Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, Pakistan
2 Department of Mathematics, University of Gujrat, Gujrat, Pakistan
doi
10.22052/ijmc.2022.243077.1584چکیده
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.
