Computing the Total Vertex Irregularity Strength Associated with Zero Divisor Graph of Commutative Ring

Ali Ahmad

Let $R$ be a commutative ring and $Z(R)$ be the set of all zero divisors of $R$. $\Gamma(R)$ is said to be a zero divisor graph if $x,y\in V(\Gamma(R))=Z(R)$ and $(x,y)\in E(\Gamma(R))$ if and only if $x.y=0.$ In this paper, we determine the total vertex irregularity strength of zero divisor graphs associated with the commutative rings $\mathbb{Z}_{p^2} ×Z_{q}$ for $p,q$ prime numbers.