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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
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