Working paper

Line Digraphs of Polytrees

Year:

2023

Published in:

SSRN
line digraph
polytree
in-tree
out-tree

We characterize line digraphs of polytrees, including several of their well-known subclasses. For a given undirected tree, we characterize its orientations with weak line digraphs, and count the exact number. Furthermore, we find the minimum, maximum, and average sizes of these line digraphs. We provide an explicit formula for the number of weak components in line digraphs of polytrees in terms of the inner sources and sinks. Additionally, we count the average number of weak components in them among all orientations of a fixed tree. Finally, we propose an algorithm for finding weak components in line digraphs of polytrees.

Related by author

12 publications found

2025
Journal article

Graphs With Odd And Even Distances Between Non‑Cut Vertices

Publisher: Opuscula Mathematica

Authors: Sergiy Kozerenko, Kateryna Antoshyna

2023
Journal article

An Optimal Lower Bound For The Size Of Periodic Digraphs

Publisher: Discrete Mathematics Letters

Authors: Sergiy Kozerenko

2016
Journal article

Markov Graphs Of One–Dimensional Dynamical Systems And Their Discrete Analogues

Publisher: Romanian Journal of Mathematics and Computer Science

Authors: Sergiy Kozerenko

2025
Journal article

On Strongly Connected Markov Graphs Of Maps On Combinatorial Trees

Publisher: Discrete Mathematics Letters

Authors: Sergiy Kozerenko

2017
Journal article

On The Abstract Properties Of Markov Graphs For Maps On Trees

Publisher: Matematicki Bilten

Authors: Sergiy Kozerenko

2024
Journal article

Dynamical Structure Of Metric And Linear Self‑Maps On Combinatorial Trees

Publisher: Discrete Mathematics Letters

Authors: Sergiy Kozerenko

2023
Journal article

Unique Eccentric Point Graphs And Their Eccentric Digraphs

Publisher: Discrete Mathematics

Authors: Sergiy Kozerenko, Artem Hak, Vladyslav Haponenko, Andrii Serdiuk

2024
Journal article

All‑Path Convexity: Two Characterizations, General Position Number, And One Algorithm

Publisher: Discrete Mathematics Letters

Authors: Sergiy Kozerenko, Vladyslav Haponenko

2020
Journal article

Periods In XOR Parallel Dynamical Systems Over Directed Dependency Graphs

Publisher: Applied Mathematics and Computation

Authors: Sergiy Kozerenko, Jose C. Valverde

2018
Journal article

On Expansive And Anti‑Expansive Tree Maps

Publisher: Opuscula Mathematica

Authors: Sergiy Kozerenko