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Mathematics 2019, 7(2), 201; https://doi.org/10.3390/math7020201

Further Results on the Resistance-Harary Index of Unicyclic Graphs

1
School of Mathematical Sciences, Anhui University, Hefei 230601, China
2
College of Mathematics, Hunan City University, Yiyang 413000, China
3
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
*
Author to whom correspondence should be addressed.
Received: 20 December 2018 / Revised: 14 February 2019 / Accepted: 14 February 2019 / Published: 20 February 2019
(This article belongs to the Special Issue Discrete Optimization: Theory, Algorithms, and Applications)
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Abstract

The Resistance-Harary index of a connected graph G is defined as R H ( G ) = { u , v } V ( G ) 1 r ( u , v ) , where r ( u , v ) is the resistance distance between vertices u and v in G. A graph G is called a unicyclic graph if it contains exactly one cycle and a fully loaded unicyclic graph is a unicyclic graph that no vertex with degree less than three in its unique cycle. Let U ( n ) and U ( n ) be the set of unicyclic graphs and fully loaded unicyclic graphs of order n, respectively. In this paper, we determine the graphs of U ( n ) with second-largest Resistance-Harary index and determine the graphs of U ( n ) with largest Resistance-Harary index. View Full-Text
Keywords: Resistance-Harary Index; resistance distance; unicyclic graphs; fully loaded unicyclic graphs Resistance-Harary Index; resistance distance; unicyclic graphs; fully loaded unicyclic graphs
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Lu, J.; Chen, S.-B.; Liu, J.-B.; Pan, X.-F.; Ji, Y.-J. Further Results on the Resistance-Harary Index of Unicyclic Graphs. Mathematics 2019, 7, 201.

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