### 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 Z

_{n}. Moreover, we also determine diameter, girth, eulerian, planar, clique number of the D[Z_{n}], ∀n. The main objective of this paper is to study interplay of ring theoretic properties of R with graph theoretic properties of D[Z_{n}].**Published:**2022-06-06

**How to 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), Article ID 169 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.

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