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

  • Lifang Zhao
  • Hongshuai Li
  • Yuping GaoEmail author


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.


Total reciprocal edge-eccentricity Cut vertex Eccentricity Degree sequence 

Mathematics Subject Classification

05C69 05C05 



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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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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