Multigroup is a generalization of a group based on the multiset structure in which repetitions of elements are allowed. The multisets are introduced to remedy the limitations of the classical set which  does not allow repetitions of elements. In this paper, we study the multigroup structure G through its associated identity-commuting graph  which is a simple graph whose vertices  are the elements of the multigroup G and two distinct vertices x and y are adjacent if and only if  and e is adjacent to all vertices of the graph, where e is the identity element. Some basic properties of this graph are studied which include: vertex degree, size, connectedness, completeness among others.

multiset, multigroup, identity graph, commuting graph.

Received: December 18, 2023; Revised: May 30, 2024; Accepted: June 21, 2024; Published: June 26, 2024

How to cite this article: S. M. Magami, M. Ibrahim, S. U. Ashafa and Gana Abubakar, Some basic properties of the identity-commuting graph of multigroups, Universal Journal of Mathematics and Mathematical Sciences 20(1) (2024), 49-71. https://doi.org/10.17654/2277141724005

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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