# Weakly nil clean graphs of rings

## TL;DR

This paper introduces the concept of weakly nil clean graphs for rings, extending previous ideas, and investigates their graph-theoretic properties such as girth, clique number, diameter, and chromatic index for finite commutative rings.

## Contribution

It generalizes the nil clean graph concept to weakly nil clean graphs and explores their properties in the context of finite commutative rings.

## Key findings

- Determined girth, clique number, diameter, and chromatic index for weakly nil clean graphs.
- Established relationships between ring properties and graph invariants.
- Extended existing graph-theoretic analyses to a broader class of rings.

## Abstract

In this article, the concept of nil clean graph of a ring has been generalised to weakly nil clean graph of a ring and graph theoretic properties like girth, clique number, diameter and chromatic index of the graph have been studied for a finite commutative ring.