Signed Product and Total Signed Product Cordial Labeling of Cartesian Product Between Balanced Bipartite Graph and Path

摘要

Nowadays, signed product cordial labeling and total signed product cordial labeling play an important role in graph labeling. For the graph G= (V,E), all the vertices are label by 1 or -1 with the restriction that the difference between total number of vertices labeled by 1 and -1 is less than equal to 1, where edge ofthe graph G= (V, E) labeled by the multiplication ofthe label ofthe end vertices also with the restriction that the difference between total number of edges labeled by 1 and -1 is less than equal to 1. We investigate some interesting result under the above labeling scheme on some new type of complex graph. In this paper, we apply signed product cordial labeling and total signed product cordial labeling on the graph obtained by Cartesian product between balanced bipartite graph K_(n,n) and path P_r. We have shown that the time complexity of the algorithms is superlinear.