Abstract
Let G be a simple, connected and undirected graph. The atom-bond connectivity index (ABC(G)) and Randić index (R(G)) are the two most well known topological indices. Recently, Ali and Du (2017) introduced the difference between atom-bond connectivity and Randić indices, denoted as ABC−R index. In this paper, we determine the fourth, the fifth and the sixth maximum chemical trees values of ABC−R for chemical trees, and characterize the corresponding extremal graphs. We also obtain an upper bound for ABC−R index of such trees with given number of pendant vertices. The role of symmetry has great importance in different areas of graph theory especially in chemical graph theory.
Highlights
Let G be a simple, connected and undirected graph. having V ( G ) and E( G ) as the set of vertices and edges respectively
In this paper, motivated by the results in [24], we further investigated the extremal chemical trees for ABC − R
We considered more maximum values of the difference ABC − R, where ABC and R
Summary
Let G be a simple, connected and undirected graph. having V ( G ) and E( G ) as the set of vertices and edges respectively. Ali and Du [24] investigated extremal binary and chemical trees results for the difference between ABC and R indices. In this paper, motivated by the results in [24], we further investigated the extremal chemical trees for ABC − R. Maximal trees with fixed number of pendant vertices are investigated for ABC − R index.
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