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

Author

Listed:
  • Lifang Zhao

    (Lanzhou University)

  • Hongshuai Li

    (Zhongshan Overseas Chinese Secondary School)

  • Yuping Gao

    (Lanzhou University)

Abstract

The total reciprocal edge-eccentricity of a graph G is defined as $$\xi ^{ee}(G)=\sum _{u\in V_G}\frac{d_G(u)}{\varepsilon _G(u)}$$ξee(G)=∑u∈VGdG(u)εG(u), where $$d_G(u)$$dG(u) is the degree of u and $$\varepsilon _G(u)$$εG(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.

Suggested Citation

  • Lifang Zhao & Hongshuai Li & Yuping Gao, 2020. "On the extremal graphs with respect to the total reciprocal edge-eccentricity," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 115-137, January.
    • Handle: RePEc:spr:jcomop:v:39:y:2020:i:1:d:10.1007_s10878-019-00458-2
    DOI: 10.1007/s10878-019-00458-2
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    References listed on IDEAS

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    1. Ailin Hou & Shuchao Li & Lanzhen Song & Bing Wei, 2011. "Sharp bounds for Zagreb indices of maximal outerplanar graphs," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 252-269, August.
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