Existence and non existence of mean cordial labeling of certain graphs

Let f be a function from the vertex set \(V (G)\) to \({0, 1, 2}\). For each edge \(uv\) assign the label \(\frac{f(u)+f(v)}{2}\). \(f\) is called a mean cordial labeling if \(|v_f (i) − v_f (j)| ≤ 1\) and \(|e_f (i) − e_f (j)| ≤ 1\), \(i, j ∈ {0, 1, 2}\), where \(v_f (x)\) and \(e_f (x)\) respectively denote the number of vertices and edges labeled with \(x\) \((x = 0, 1, 2)\). A graph with a mean cordial labeling is called a mean cordial graph. In this paper we investigate mean cordial labeling behavior of prism, \(K_2 +\overline{K_m}\), \(K_n + \overline{2K_2}\), book \(B_m\) and some snake graphs.