ALGORITHMIC APPROACH OF CORDIAL LABELING ON CARTESIAN PRODUCT BETWEEN BALANCED BIPARTITE GRAPH AND PATH

Abstract

Cordial labeling is one of the useful labeling in the realm of graphlabeling. For the graph G = (V; E) vertex set V is label by f0; 1g, wherelabeling of edge set E calculated by absolute di§erence between the end verticeslabeling with the restriction that number of vertices label by 0 and numberof vertices label by 1, their absolute di§erence not exceeding 1. If similarrestriction will follow for edge also then the labeling technique is known ascordial labeling and the graph which admits cordial labeling is known as cordialgraph. In this paper we want to apply cordial labeling on a complex graphstructure which we obtained by Cartesian product between complete bipartitegraph(Balanced bipartite graph) Kn;n and path Pr. We also propose threealgorithm to label the above said graph by cordial labeling. We have analysethe time complexity of each algorithm and which is super-linear.