Further Results on the Resistance-Harary Index of Unicyclic Graphs
School of Mathematical Sciences, Anhui University, Hefei 230601, China
College of Mathematics, Hunan City University, Yiyang 413000, China
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
The Resistance-Harary index of a connected graph G
is defined as
is the resistance distance between vertices u
. 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
be the set of unicyclic graphs and fully loaded unicyclic graphs of order n
, respectively. In this paper, we determine the graphs of
with second-largest Resistance-Harary index and determine the graphs of
with largest Resistance-Harary index.
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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.
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(2):201.
Lu, Jian; Chen, Shu-Bo; Liu, Jia-Bao; Pan, Xiang-Feng; Ji, Ying-Jie. 2019. "Further Results on the Resistance-Harary Index of Unicyclic Graphs." Mathematics 7, no. 2: 201.
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