On the divisor graph of finite commutative ring
Abstract
In this paper, we introduce a graphical structure of non empty finite commutative ring R called as divisor graph of R, denoted as D[R], is undirected simple graph with vertex set V=R−{0,1} and for distinct vertices a,b∈V, a∼b if and only if either a|b or b|a, i.e. ∃c∈R such that a=bc or b=ac. We will discuss structure and properties of divisor graph of ring Zn. Moreover, we also determine diameter, girth, eulerian, planar, clique number of the D[Zn], ∀n. The main objective of this paper is to study interplay of ring theoretic properties of R with graph theoretic properties of D[Zn].
Copyright © 2022 P. D. Khandare, S. M. Jogdand, R. A. Muneshwar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
P. D. Khandare, S. M. Jogdand, R. A. Muneshwar, On the divisor graph of finite commutative ring, J. Math. Comput. Sci. 12 (2022), 169. https://doi.org/10.28919/jmcs/7209
BibTeX
@article{Khandare2022,
author = {Khandare, P. D. and Jogdand, S. M. and Muneshwar, R. A.},
title = {On the divisor graph of finite commutative ring},
journal = {J. Math. Comput. Sci.},
volume = {12},
year = {2022},
pages = {169},
doi = {10.28919/jmcs/7209}
}