Abstract
The ladder graph \(L_n\) is the Cartesian product of a path on n vertices and a complete graph on two vertices. The Wiener index of a digraph is the sum of distances between all ordered pairs of vertices. In Knor et al. (Bounds in chemical graph theory - advances, 2017) the authors conjectured that the maximum Wiener index of a digraph whose underlying graph is \(L_n\) is \((8n^3+3n^2-5n+6)/3\). In this article we prove the conjecture.
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Acknowledgements
Authors were partially supported by Slovenian research agency ARRS, first two under the grants J1-9109 and P1-0297 and third author under the grant J1-9109.
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Šumenjak, T.K., Špacapan, S. & Štesl, D. A proof of a conjecture on maximum Wiener index of oriented ladder graphs. J. Appl. Math. Comput. 67, 481–493 (2021). https://doi.org/10.1007/s12190-021-01498-w
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DOI: https://doi.org/10.1007/s12190-021-01498-w