On New Thue Colouring Concepts of Certain Graphs
Johan Kok, Erika Skrabulakova, Naduvath Sudev

TL;DR
This paper introduces new concepts in Thue graph colouring, focusing on how edge removal affects the Thue number and proposing a measure for the efficiency of such modifications.
Contribution
It defines the $ au$-index as a novel measure to evaluate the effectiveness of edge deletions in reducing the Thue chromatic number of graphs.
Findings
Analysis of the change in Thue number with edge removal
Introduction of the $ au$-index as an efficiency measure
Insights into graph colouring stability under edge deletions
Abstract
The Thue colouring of a graph is a colouring such that the sequence of vertex colours of any path of even and finite length in is non-repetitive. The change in the Thue number, , as edges are iteratively removed from a graph is studied. The notion of the -index denoted, , of a graph is introduced as well. serves as a measure for the efficiency of edge deletion to reduce the Thue chromatic number of a graph.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · semigroups and automata theory
