Prime labelling of centerless double wheel graph using Python programming
Date
2024-11-01
Authors
Herath, H. M. O. D.
Weerarathna, M. D. M. C. P.
Perera, A. A. I.
Journal Title
Journal ISSN
Volume Title
Publisher
Postgraduate Institute of Science (PGIS), University of Peradeniya, Sri Lanka
Abstract
This research investigated the prime labelling of the Centerless Double Wheel graph (๐ถ๐ทWโ๐ ) using Python programming. Prime labelling is a type of graph labelling that assigns labels to graph vertices such that the greatest common divisor of the labels of adjacent vertices is one. While most previous works on prime labelling have largely relied on manual methods to assign values to vertices based on specific conditions, this study automates the labelling process through programming. The Centerless Double Wheel graph is a simple graph obtained by using the Cartesian product of Cyclic graph; C๐ with ๐ vertices and Complete graph of the form kโ and is denoted by ๐ถ๐ทWโ๐ (i.e. ๐ถ๐รkโ=๐ถ๐ท๐โ๐). If ๐ is an even integer, then ๐ถ๐ท๐โ๐ achieve its prime labelling based on whether ๐+1 is prime, or, 2๐+1 is prime. Contrarily, this study established that no prime labelling exists for ๐ถ๐ท๐โ๐ when ๐ is odd. The proof of the theorem is given as a combinatorial version, and the algorithmic approach was detailed using Python, offering a step-by-step procedure for generating and labelling ๐ถ๐ท๐โ๐ graphs. This work advances the understanding of prime graph labelling and provides computational tools to simplify the process, setting a foundation for future exploration of more complex graph structures.
Description
Keywords
Centerless Double Wheel graph , Prime labelling , Python programming
Citation
Proceedings of the Postgraduate Institute of Science Research Congress (RESCON) -2024, University of Peradeniya, P 49