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Open AccessArticle

Maximum Detour–Harary Index for Some Graph Classes

1
College of Information & Network Engineering, Anhui Science and Technology University, Fengyang 233100, China
2
College of Information and Management Science, Henan Agricultural University, Zhengzhou 450002, China
3
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
4
Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu 233030, China
5
School of Finance, Anhui University of Finance and Economics, Bengbu 233030, China
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(11), 608; https://doi.org/10.3390/sym10110608
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)
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PDF [466 KB, uploaded 7 November 2018]
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Abstract

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
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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.

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