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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...
From investigating graphical passwords (NGPs), we define set-labellings and set-colorings (set-labelling/colorings) of networks/graphs, and define the new edge-colorings called adjacent 1-common edge-coloring and vertex 1-common edge-coloring. Some connections between traditional graph colorings and our set-labelling/colorings are found. Conversely, our results can be used to design more complicated...
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...
New passwords obtained by an idea of "graphical construction plus number theory" could be easy than other graphical passwords in storage space and communication of information. We show two examples for illustrating this idea, and design a new graph labelling, called (k +, k -)-couple edge- magic total labelling, for realizing possibly this idea. We then present some theoretical algorithms...
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