On coloring/labelling graphical groups for creating new graphical passwords

Graphical passwords are possibly alternative for text-based passwords. The idea of “graphical structure plus number theory” (GSpNT) for creating new type of graphical passwords has been investigated, since the new graphical passwords made by GSpNT needs less storage and implements quickly in network communication. We try to find some connections between new graphical passwords defined on a topological structure, and show some them can form algebraic groups in this article. By the way, we find new graph labellings in which some mathematical conjectures are produced.