期刊论文

Liu, Jia-Bao

英文

Mathematics

2227-7390

2019

7

2

201-

10.3390/math7020201

Funding Acquisition, J.L. and J.-B.L.; Methodology, J.-B.L. and J.L.; Supervision, X.-F.P.; and Writing—Original Draft, J.L. and S.-B.C. All authors read and approved the final manuscript. This work was supported by the National Natural Science Foundation of China (11601006), the China Postdoctoral Science Foundation (2017M621579), the Postdoctoral Science Foundation of Jiangsu Province (1701081B), the Project of Anhui Jianzhu University (2016QD116 and 2017dc03) and the Anhui Province Key Laboratory of Intelligent Building and Building Energy Saving.

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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 ) w...