Further Results on the Resistance-Harary Index of Unicyclic Graphs

Jian Lu, Shu-Bo Chen, Jia-Bao Liu, Xiang-Feng Pan and Ying-Jie Ji
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Jian Lu: School of Mathematical Sciences, Anhui University, Hefei 230601, China
Shu-Bo Chen: College of Mathematics, Hunan City University, Yiyang 413000, China
Jia-Bao Liu: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Xiang-Feng Pan: School of Mathematical Sciences, Anhui University, Hefei 230601, China
Ying-Jie Ji: School of Mathematical Sciences, Anhui University, Hefei 230601, China

Mathematics, 2019, vol. 7, issue 2, 1-13

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.

Keywords: Resistance-Harary Index; resistance distance; unicyclic graphs; fully loaded unicyclic graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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