Next Article in Journal
Navigating Non-Playable Characters Based on User Trajectories with Accumulation Map and Path Similarity
Next Article in Special Issue
Nordhaus–Gaddum-Type Results for the Steiner Gutman Index of Graphs
Previous Article in Journal
Dual Attention-Guided Multiscale Dynamic Aggregate Graph Convolutional Networks for Skeleton-Based Human Action Recognition
Previous Article in Special Issue
Computational Properties of General Indices on Random Networks
Open AccessArticle

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

1
Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Terengganu, Malaysia
2
School of Software, South China Normal University, Foshan 528225, China
3
School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, China
4
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; https://doi.org/10.3390/sym12101591
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
Show Figures

Figure 1

MDPI and ACS Style

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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop