On the Clean Graph of a Ring
Combinatorics
2023-01-24 v1
Abstract
Let R be a ring (not necessarily commutative ring) with identity. The clean graph Cl(R) of a ring R is a graph with vertices in the form of ordered pair (e; u), where e is an idempotent of the ring R and u is a unit of the ring R. Two distinct vertices (e; u) and (f; v) are adjacent if and only if ef = fe = 0 or uv = vu = 1. In this paper, we determine the Wiener index, Matching number of the clean graph of the ring Zn.
Keywords
Cite
@article{arxiv.2301.09433,
title = {On the Clean Graph of a Ring},
author = {Randhir Singh and S. C. Patekar},
journal= {arXiv preprint arXiv:2301.09433},
year = {2023}
}