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The maximum Wiener index of maximal planar graphs
Journal of Combinatorial Optimization ( IF 1 ) Pub Date : 2020-10-03 , DOI: 10.1007/s10878-020-00655-4 Debarun Ghosh , Ervin Győri , Addisu Paulos , Nika Salia , Oscar Zamora
中文翻译:
最大平面图的最大维纳指数
更新日期:2020-10-04
Journal of Combinatorial Optimization ( IF 1 ) Pub Date : 2020-10-03 , DOI: 10.1007/s10878-020-00655-4 Debarun Ghosh , Ervin Győri , Addisu Paulos , Nika Salia , Oscar Zamora
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 \(\lfloor \frac{1}{18}(n^3+3n^2)\rfloor \). We prove this conjecture and determine the unique n-vertex maximal planar graph attaining this maximum, for every \( n\ge 10\).
中文翻译:
最大平面图的最大维纳指数
连通图的维纳指数是图中所有顶点对之间距离的总和。推测n个顶点最大平面图的Wiener索引最多为\(\ lfloor \ frac {1} {18}(n ^ 3 + 3n ^ 2)\ rfloor \)。我们证明这个猜想,并针对每个\(n \ ge 10 \)确定达到此最大值的唯一n-顶点最大平面图。