Next Article in Journal
A Fuzzy Classifier with Feature Selection Based on the Gravitational Search Algorithm
Next Article in Special Issue
Novel Three-Way Decisions Models with Multi-Granulation Rough Intuitionistic Fuzzy Sets
Previous Article in Journal
A Coarse-to-Fine Fully Convolutional Neural Network for Fundus Vessel Segmentation
Previous Article in Special Issue
Q-Filters of Quantum B-Algebras and Basic Implication Algebras
Open AccessArticle

Maximum Detour–Harary Index for Some Graph Classes

College of Information & Network Engineering, Anhui Science and Technology University, Fengyang 233100, China
College of Information and Management Science, Henan Agricultural University, Zhengzhou 450002, China
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, China
School of Finance, Anhui University of Finance and Economics, Bengbu 233030, China
Author to whom correspondence should be addressed.
Symmetry 2018, 10(11), 608;
Received: 12 September 2018 / Revised: 19 October 2018 / Accepted: 22 October 2018 / Published: 7 November 2018
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
PDF [466 KB, uploaded 7 November 2018]


The definition of a Detour–Harary index is ω H ( G ) = 1 2 u , v V ( G ) 1 l ( u , v | G ) , where G is a simple and connected graph, and l ( u , v | G ) is equal to the length of the longest path between vertices u and v. In this paper, we obtained the maximum Detour–Harary index about unicyclic graphs, bicyclic graphs, and cacti, respectively. View Full-Text
Keywords: Detour–Harary index; maximum; unicyclic; bicyclic; cacti Detour–Harary index; maximum; unicyclic; bicyclic; cacti

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Fang, W.; Liu, W.-H.; Liu, J.-B.; Chen, F.-Y.; Hong, Z.-M.; Xia, Z.-J. Maximum Detour–Harary Index for Some Graph Classes. Symmetry 2018, 10, 608.

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.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top