Group {1, −1, i, −i} Cordial Labeling of Product Related Graphs

Let G be a (p,q) graph and A be a group. Let f : V (G) → A be a function. The order of u ∈ A is the least positive integer n such that un = e. We denote the order of u by o(u). For each edge uv assign the label 1 if (o(u), o(v)) = 1 or 0 otherwise. f is called a group A Cordial labeling if |vf (a) − vf (b)| ≤ 1 and |ef (0) − ef (1)| ≤ 1, where vf (x) and ef (n) respectively denote the number of vertices labeled with an element x and number of edges labeled with n(n = 0, 1). A graph which admits a group A Cordial labeling is called a group A Cordial graph. In this paper we define group {1,−1, i,−i} Cordial graphs and prove that Hypercube Qn = Qn−1 × K2, Book Bn = Sn × K2, n-sided prism Prn = Cn × K2 and Pn × K3 are all group {1,−1, i,−i} Cordial for all n.