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The maximum Wiener index of maximal planar graphs

Author

Listed:
  • Debarun Ghosh

    (Central European University)

  • Ervin Győri

    (Central European University
    Alfréd Rényi Institute of Mathematics)

  • Addisu Paulos

    (Central European University
    Addis Ababa University)

  • Nika Salia

    (Central European University
    Alfréd Rényi Institute of Mathematics)

  • Oscar Zamora

    (Central European University
    Universidad de Costa Rica)

Abstract

The Wiener index of a connected graph is the sum of the distances between all pairs of vertices in the graph. It was conjectured that the Wiener index of an n-vertex maximal planar graph is at most $$\lfloor \frac{1}{18}(n^3+3n^2)\rfloor $$ ⌊ 1 18 ( n 3 + 3 n 2 ) ⌋ . We prove this conjecture and determine the unique n-vertex maximal planar graph attaining this maximum, for every $$ n\ge 10$$ n ≥ 10 .

Suggested Citation

  • Debarun Ghosh & Ervin Győri & Addisu Paulos & Nika Salia & Oscar Zamora, 2020. "The maximum Wiener index of maximal planar graphs," Journal of Combinatorial Optimization, Springer, vol. 40(4), pages 1121-1135, November.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:4:d:10.1007_s10878-020-00655-4
    DOI: 10.1007/s10878-020-00655-4
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    References listed on IDEAS

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    1. Kinkar Ch. Das & M. J. Nadjafi-Arani, 2017. "On maximum Wiener index of trees and graphs with given radius," Journal of Combinatorial Optimization, Springer, vol. 34(2), pages 574-587, August.
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