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arXiv · 2205.13752

On Lyndon-Word Representable Graphs

Hossein Teimoori Faal
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Abstract

In this short note, we first associate a new simple undirected graph with a given word over an ordered alphabet of $n$-letters. We will call it the Lyndon graph of that word. Then, we introduce the concept of the Lyndon-word representable graph as a graph isomorphic to a Lyndon graph of some word. Then, we introduce the generalized Stirling cycle number $S(N;n,k)$ as the number words of length $N$ with $k$ distinct Lydon words in their Lyndon factorization over an ordered alphabet of $n$-letters . Finally, we conclude the paper with several interesting open questions and conjectures for interested audiences.

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Hossein Teimoori Faal. 2022-05-27. On Lyndon-Word Representable Graphs. https://arxiv.org/abs/2205.13752

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