On 3-total edge product cordial labeling of grid

Let us consider a mapping ϕ:E(G) →{0, 1,…,k − 1} of a graph G, where k is an integer, 2 ≤ k ≤|E(G)|. The mapping ϕ induces for every vertex v of G the label ϕ∗(v) =∏ uv∈E(G)ϕ(uv)(modk). Let eϕ(i) (...