The Cordiality for the Conjunction of Two Paths

Abstract A graph is called cordial if it has a 0 - 1 labeling such that the number of vertices (edges) labeled with ones and zeros dier by at most one. The conjunction of two graphs (V1;E1) and (V2;E2) is the graph G = (V;E), where V = V1 x V2 and u = (a1; a2), v = (b1; b2) are two vertices, then uv belongs to E if aibi belongs to Ei for i = 1 or 2. In this paper, we present necessary and sucient condition for cordial labeling for the conjunction of two paths, denoted by Pn ^ Pm. Also, we drive an algorithm to generate cordial labeling for the conjunction Pn ^ Pm.