Linear Arrangement of Halin Graphs

TL;DR

This paper investigates the optimal linear arrangement problem for Halin graphs, establishing bounds, properties, and efficient algorithms for specific classes, advancing understanding of graph arrangement complexities.

Contribution

It provides new properties, bounds, and an O(n log n) algorithm for certain Halin graphs' optimal linear arrangements.

Findings

Lower bound on OLA cost for Halin graphs

Identification of classes where OLA matches the lower bound

Efficient O(n log n) algorithm for specific Halin graph classes

Abstract

We study the Optimal Linear Arrangement (OLA) problem of Halin graphs, one of the simplest classes of non-outerplanar graphs. We present several properties of OLA of general Halin graphs. We prove a lower bound on the cost of OLA of any Halin graph, and define classes of Halin graphs for which the cost of OLA matches this lower bound. We show for these classes of Halin graphs, OLA can be computed in O(n log n), where n is the number of vertices.