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On the extremal graphs with respect to the total reciprocal edge-eccentricity

  • Lifang Zhao
  • Hongshuai Li
  • Yuping GaoEmail author
Article
First Online:
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Abstract

The total reciprocal edge-eccentricity of a graph G is defined as \(\xi ^{ee}(G)=\sum _{u\in V_G}\frac{d_G(u)}{\varepsilon _G(u)}\), where \(d_G(u)\) is the degree of u and \(\varepsilon _G(u)\) is the eccentricity of u. In this paper, we first characterize the unique graph with the maximum total reciprocal edge-eccentricity among all graphs with a given number of cut vertices. Then we determine the k-connected bipartite graphs of order n with diameter d having the maximum total reciprocal edge-eccentricity. Finally, we identify the unique tree with the minimum total reciprocal edge-eccentricity among the n-vertex trees with given degree sequence.

Keywords

Total reciprocal edge-eccentricity Cut vertex Eccentricity Degree sequence 

Mathematics Subject Classification

05C69 05C05 
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Notes

Acknowledgements

The authors wish to thank the anonymous referees for their careful reading and valuable comments on how to improve this paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsLanzhou UniversityLanzhouPeople’s Republic of China
  2. 2.Zhongshan Overseas Chinese Secondary SchoolZhongshanPeople’s Republic of China

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