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

Abstract

Let R be a commutative ring and Z(R) be the set of all zero divisors of R. Γ(R) is said to be a zero divisor graph if x,y ∈ V (Γ(R)) = Z(R) and (x,y) ∈ E(Γ(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 ℤp2 × Zq for p,q prime numbers.