Coprime Graph of Multigroup over the Dihedral Group D2n, n ≥ 3 where n is prime
DOI:
https://doi.org/10.33003/fjs-2026-1009-3780Keywords:
Multigroup, Coprime Graph, Complete Graph, Multipartite, Mul;tisetAbstract
Multigroups are structures that generalize groups and are obtained from multisets. Multisets are sets in which element can occur more than once which were introduced to help with real-life situations, repetition of elements is inevitable.
The coprime graph of a multigroup , is any graph with as its vertex set and two distinct vertices and are connected by an edge if and only if . In this paper, we carry out study of multigroup over the dihedral group using the coprime graph associated with it. Some basic properties of the coprime graph were studied which include: vertex degree, size, connectedness, completeness among others. It was shown that the graph is connected and can never be a complete graph. The clique number and chromatic number of the graph were obtained.
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Copyright (c) 2026 Umar Ashafa Sulaiman, Gana Abubakar
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