Modular irregular labelling in Network Analysis with Complete Bipartite Graph as Auto Proctoring

Modular irregular labeling is an edge irregular labeling of a graph in which the edges and vertices are labelled with 1, 2, 3,.. k such that the weight of all vertices are different. The complete bipartite graph is whose vertices are divided into two subsets such that no edge is in the same subset. In this paper the modular irregular labeling technique is applied in the complete bipartite graph. It is also planned to develop certain theorems in work of applying the modular irregular labeling in complete bipartite graph. An application in complete bipartite graph in the field of networking is also discussed. The aim of the work is to build the theorem and to promote an application in complete bipartite graph. The application is about the autoproctor for the online examination to make work easier for the examiner to examine students.