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Open AccessArticle

Extremal Trees with Respect to the Difference between Atom-Bond Connectivity Index and Randić Index

Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia
School of Software, South China Normal University, Foshan 528225, China
School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China
Department of Mathematics, Riphah Institute of Computing and Applied Sciences, Riphah International University, Lahore 46000, Pakistan
Author to whom correspondence should be addressed.
Symmetry 2020, 12(10), 1591;
Received: 23 July 2020 / Revised: 20 August 2020 / Accepted: 23 August 2020 / Published: 25 September 2020
(This article belongs to the Special Issue Analytical and Computational Properties of Topological Indices)
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 ABCR index. In this paper, we determine the fourth, the fifth and the sixth maximum chemical trees values of ABCR for chemical trees, and characterize the corresponding extremal graphs. We also obtain an upper bound for ABCR 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. View Full-Text
Keywords: Randić index; Atom-bond connectivity index; tree Randić index; Atom-bond connectivity index; tree
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Zuki, W.N.N.N.W.; Du, Z.; Kamran Jamil, M.; Hasni, R. Extremal Trees with Respect to the Difference between Atom-Bond Connectivity Index and Randić Index. Symmetry 2020, 12, 1591.

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