Title of article :
Maximum Variable Connectivity Index of n-Vertex Trees
Author/Authors :
YOUSAF , SHAMAILA Department of Sciences and Humanities - National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, Pakistan , AHMAD BHATTI, AKHLAQ Department of Sciences and Humanities - National University of Computer and Emerging Sciences, Lahore Campus, B-Block, Faisal Town, Lahore, Pakistan
Abstract :
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
∑ (( )( ))
⁄
,
where
is a non-negative real number and
is the degree of
vertex
in . The main objective of the present study is to prove
the conjecture proposed in [19]. In this study, we will show that the
(path graph) has the maximum variable connectivity index
among the collection of trees whose order is , where .
Keywords :
Chemical graph theory , Variable connectivity index , Variable Randić index , Trees , Extremal problem
Journal title :
Iranian Journal of Mathematical Chemistry
