Abstract
Topological indices have important effect to develop chemical sciences by using graph invariants. The Zagreb indices are the most used topological indices in mathematical chemistry literature. Novel forms of Zagreb indices have been extensively defined in recent times. One of the latest version of the Zagreb indices is the reverse Zagreb alpha index. Extremal chemical trees with respect to Zagreb indices have been studied many times in the last two years. In this paper maximum chemical trees were characterized with respect to the first reverse Zagreb alpha index.
Highlights
Graph theory which is one of the most important branches of applied mathematics has many applications related to chemical and biological sciences
From this, it was got that n1 − n2 − n3 + n4 = 3r −1. If we subtract this last equality from the Equation 2, it was acquired that n2 + n3 = 1 which is a contradiction to the for n = 3r + 1 ( r ≥ 2 ), if G is nvertex chemical tree, CM1α (G) ≤ 11n + 8 and equality is attained if and only if there are r − 1 vertices of degree 4, one vertex of degree 3 and remaining vertices are pendant
For n = 3r + 2 ( r ≥ 2 ), if G is n-vertex chemical tree, CM1α (G) ≤ 11n + 8 and equality is attained if and only if there are r vertices of degree 4 and the remaining vertices are pendant
Summary
Graph theory which is one of the most important branches of applied mathematics has many applications related to chemical and biological sciences. More than forty years ago Gutman & Trinajstić (1971) defined Zagreb indices which are degree based topological indices [2] These topological indices were proposed to be measures of Süleyman Ediz: Extremal Chemical Trees of the First Reverse Zagreb Alpha Index branching of the carbon-atom skeleton in [3]. The reverse vertex degree of a vertex v of a simple connected graph G defined as; cv = ∆ − dv +1 where ∆ denotes the largest of all degrees of vertices of G and dv denotes the number of edges incident to v. Extremal trees and graphs with respect to total reverse vertex degree and first reverse Zagreb alpha index have been characterized in [12]. The aim of this paper is to characterize maximum chemical trees with respect to the first reverse Zagreb alpha index
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