Algorithmic approach of cordial labeling on Cartesian product between balanced bipartite graph and path

Cordial labeling is one of the useful labeling in the realm of graph labeling. For the graph G=(V,E) vertex set V is label by {0,1}, where labeling of edge set E calculated by absolute difference between the end vertices labeling with the restriction that number of vertices label by 0 and number of vertices label by 1, their absolute difference not exceeding 1. If similar restriction will follow for edge also then the labeling technique is known as cordial labeling and the graph which admits cordial labeling is known as cordial graph. In this paper we want to apply cordial labeling on a complex graph structure which we obtained by Cartesian product between complete bipartite graph(Balanced bipartite graph) K_{n,n} and path P_{r}. We also propose three algorithm to label the above said graph by cordial labeling. We have analyse the time complexity of each algorithm and which is super-linear.