论文信息 - Mean distance in a tree

Mean distance in a tree

Abstract We characterize the quantities which can arise as the mean distance in a tree, giving in each case the number of nonisomorphic trees with the given mean distance. In particular, we show that every rational r≥2 is the mean distance in some tree, solving a problem posed by Hendry.

Peter Winkler

[1] Mirosław Truszczyński. A GRAPH WITH MEAN DISTANCE BEING A GIVEN RATIONAL , 1985 .

[2] L. Lovász. Combinatorial problems and exercises , 1979 .

[3] G. R. T. Hendry. Existence of graphs with prescribed mean distance , 1986, J. Graph Theory.

[4] Bruce Reznick. The sum of the squares of the parts of a partition, and some related questions , 1989 .

[5] Ján Plesník,et al. On the sum of all distances in a graph or digraph , 1984, J. Graph Theory.

[6] J. K. Doyle,et al. Mean distance in a graph , 1977, Discret. Math..