Group {1, −1, i, −i} Cordial Labeling of Some Special Graphs

Abstract

Let G be a (p,q)graph and A be a group. Let f : V (G) → A be a function. The order of a ∈ A is the least positive integer n such that a n = e. We denote the order of a by o(a). For each edge uv assign the label 1 if (o(u), o(v)) = 1or 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 Double fan DFn, Wn,n, closed helm CHn, Gear graph Gn and the web graph W(2, n) are all group {1, −1, i, −i} Cordial for evey n.