k-Total mean cordial graphs

Let G be a (p,q) graph. Let f: V (G) → {0,1,2,3,..., k −1} be a function where k ∈ N and k > 1. For each edge uv, assign the label f(uv) = ⌈f(u)+f(v)/2⌉. f is called k-total mean cordial labeling of G if |tm f(i)−tm f(j)| ≤ 1, i, j ∈ {0,1,2,..., k −1}, where tm f(x) denotes the total number of vertices and edges labelled with x, x ∈ {0,1,2,..., k −1}. A graph with admit a k-total mean cordial labeling is called k-total mean cordial graph.