Total 3-sum cordial labeling on zero divisor graphs

Consider g : V (G) → {0, 1, 2} such that |ν_g(ℓ) − ν_g(j)| ≤ 1 and |e_g(ℓ) − e_g(j)| ≤ 1 for any ℓ, j ∈ {0, 1, 2}, where ν_g(ℓ) denotes the number of vertices labeled with ℓ, e_g(ℓ) denotes the number of edges ηβ with (g(η) + g(β)) ≡ ℓ (mod 3). Then g is called total 3-sum cordial labeling. A graph with a total 3-sum cordial labeling is called a total 3-sum cordial graph. We study the total 3-sum cordial labeling of zero-divisor graphs.