Group {1, -1, i, -i} Cordial Labeling of Some Shadow Graphs

M. K. Karthik Chidambaram, S. Athisayanathan, R. Ponraj

Abstract: 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(f (u)), o(f (v))) = 1 or 0 otherwise. The function 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. The Shadow graph D2(G) of a connected graph G is constructed by taking two copies of G, G? and G? and joining each vertex u? in G? to the neighbours of the corresponding vertex u? in G?. In this paper we define group {1, ?1, i, ?i} Cordial graphs and prove that the Shadow graphs of Path Pn and Cycle Cn are group {1, ?1, i, ?i} Cordial. We also characterize shadow graph of Complete graph Kn that are group {1, ?1, i, ?i} Cordial.

Keywords: Cordial labeling, group A Cordial labeling, group {1, -1, i, -i} Cordial labeling, Shadow graph