On Topological Graphic Passwords Made by Twin Edge Module-k Odd-Graceful Labelling

Abstract

Graphic password has been widely used in mobile devices and other fields, and it is facing a good opportunity for development since QR code is welcomed in the world. Here is a new graphical password (Topsnut-GPW) based on the idea of “topological structure plus number theory” and various labellings for solving network transfer delay by using other type of graphical passwords. The new Topsnut-GPW has been designed by technique of graph theory. We define a new labelling, called twin edge module-k odd-graceful labelling, for producing our Topsnut-GPWs that can form algebraic groups, called the labelled graphical groups. Our methods can be transformed into effective algorithms.