Computation of twin-width of graphs

TL;DR

This paper investigates the twin-width of finite graphs, providing exact values for small graphs, examining how certain graph operations affect twin-width, and establishing upper bounds for specific graph classes.

Contribution

It computes twin-width for small graphs, analyzes the impact of dual and line graph constructions, and offers bounds for King's and Rook's graphs.

Findings

Twin-width of graphs with 4 vertices is at most 1.

Twin-width of graphs with 5 vertices is at most 2.

Dual and line graph constructions do not preserve twin-width.

Abstract

Twin-width is a recently introduced graph parameter. In this article, we compute twin-width of various finite graphs. In particular, we prove that the twin-widths of finite graphs with 4 and 5 vertices are less than equal to 1 and 2, respectively. We show that the constructions of dual graph and line graph do not preserve twin-width. Also, we give upper bounds for the twin-width of King's graph and Rook's graph.