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Path vectors and optimal trees. (English) Zbl 0918.05072

The path vector of a digraph \(D\) on \(n\) vertices is the \((n-1)\)-vector \((d_1(D),\dots,d_{n-1}(D))\), where \(d_i(D)\) denotes the number of directed paths of length \(i\) in \(D\). This paper studies path vectors of oriented trees and a certain dominance relation based on path vectors.

MSC:

05C38 Paths and cycles
05C35 Extremal problems in graph theory
05C20 Directed graphs (digraphs), tournaments
05C05 Trees
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