Exploring new graphical passwords by graph set-colorings subject to constraint sets

摘要

For the purpose of producing more complex graphical passwords by means of smaller graphs having fewer numbers of vertices and edges for easily be remembered and difficultly be break down, we prove: (1) a tree T having n vertices has a strongly set-coloring subject to the constraint set of six restrict conditions; (2) a connected (p,q)-graph G has a strongly set-coloring subject to the constraint set of eight restrict conditions. The proof methods used in this article can be transferred into efficient algorithms.