Colourability of graphs representing the Lucas series modulo t

Preen, James; McGillivray, Claire

doi:10.2140/involve.2023.16.719

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Colourability of graphs representing the Lucas series modulo $t$

James Preen and Claire McGillivray

Vol. 16 (2023), No. 4, 719–726

DOI: 10.2140/involve.2023.16.719

Abstract

Given a sequence we can define a directed graph using the values of the sequence as vertices and joining consecutive vertices by arcs. The graph formed from the Lucas numbers modulo $t$ is proved to be properly colourable with two colours if $t$ is either a multiple of 5 or a Fibonacci number greater than 13.

Keywords

Lucas, Fibonacci, graph, colouring

Mathematical Subject Classification

Primary: 11B39

Secondary: 05C15

Milestones

Received: 10 September 2022

Accepted: 18 October 2022

Published: 31 October 2023

Communicated by Arthur T. Benjamin

Authors

James Preen
Department of Mathematics, Physics and Geology Cape Breton University Sydney, NS Canada

Claire McGillivray
Cape Breton University Sydney, NS Canada

Vol. 16, No. 4, 2023