Applying graph set-labellings having constraint sets towards new graphical passwords

Motivated from the idea of "graphical structure plus number theory", two new set-colorings subject to some constraint sets are defined: one is the strong set-coloring (F, F') with the edge set-labelling F' induced by the vertex set-labelling F, and other one is the strongly total set-coloring. We show that every simple, connected (p,q)-graph G admits a strongly total set-labelling, and any tree having a super edge-magic total labelling admits a 2-uniform strongly total set-coloring.