Group {1,–1,i,–i} Cordial Labeling of Some New Graphs

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

Page No: 187-196

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. 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 the Sunflower graph SFn , the graph Lotus inside a circle LCn , the Umbrella graph Un,n are all group {1,–1,i,–i} Cordial for all n. We further characterize Jewel graphs that are group {1,–1,i,–i} Cordial.

Authors :
M.K.Karthik Chidambaram, S. Athisayanathan & R.Ponraj : Department of Mathematics, St. Xavier’s College , Palayamkottai 627 002, Tamil Nadu, India.