Abstract: For a finite ring with unity R, we define a simple undirected graph called the codivisor graph with all the non-zero elements of the ring R as vertices and two distinct vertices a and b are adjacent to each other if and only if and We first consider its connectedness. Looking at we determine the condition for connectedness of and also discuss its structure. We further investigate properties like diameter, girth, completeness, planarity, traversability, independence number and domination number in our work.
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Keywords and phrases: integers modulo n, coprime set, complete graph, diameter, girth.
Received: March 4, 2023; Revised: April 28, 2023; Accepted: May 12, 2023; Published: June 2, 2023
How to cite this article: Anurag Baruah and Kuntala Patra, The codivisor graph of a finite ring with unity, Advances and Applications in Discrete Mathematics 39(2) (2023), 169-181. http://dx.doi.org/10.17654/0974165823044
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
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