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Colourability
of graphs representing the Lucas series modulo $t$
James Preen and Claire McGillivray |
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Vol. 16 (2023), No. 4, 719–726
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Abstract |
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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 is proved to be properly colourable with two colours if is either a multiple of 5 or a Fibonacci number greater than 13. |
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Keywords
Lucas, Fibonacci, graph, colouring
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Mathematical Subject Classification
Primary: 11B39
Secondary: 05C15
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Milestones
Received: 10 September 2022
Accepted: 18 October 2022
Published: 31 October 2023
Communicated by Arthur T. Benjamin
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Authors |
| James Preen | |
| Department of Mathematics, Physics
and Geology Cape Breton University Sydney, NS Canada |
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| Claire McGillivray | |
| Cape Breton University Sydney, NS Canada |
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| © 2023 MSP (Mathematical Sciences Publishers). |
