The maximum Wiener index of maximal planar graphs

Debarun Ghosh (), Ervin Győri (), Addisu Paulos (), Nika Salia () and Oscar Zamora ()
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Debarun Ghosh: Central European University
Ervin Győri: Central European University
Addisu Paulos: Central European University
Nika Salia: Central European University
Oscar Zamora: Central European University

Journal of Combinatorial Optimization, 2020, vol. 40, issue 4, No 16, 1135 pages

Abstract: 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 .

Keywords: Wiener index; Planar graphs; Triangulation; Distance; Mini–Max (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10878-020-00655-4

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