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Graph labellings have been applied in many areas of science and engineering, such as in the development of redundant arrays of independent disks which incorporate redundancy utilizing erasure codes, algorithms, design of highly accurate optical gauging systems for use on automatic drilling machines, design of angular synchronization codes, design of optimal component layouts for certain circuit-board geometries, and determining configurations of simple resistor networks which can be used to supply any of a specified set of resistance values. Based on the idea of of “topological structure plus number theory” and magic type of various labellings for solving network transfer delay by using other type of graphical passwords. We define a new graph labelling, called Module-K odd-elegant labelling, and find some network models that admit our new labelling, and furthermore our methods can be transformed into effective algorithms

Graph Theory Towards Module-K Odd-Elegant Labelling Of Graphical Passwords