Edge-difference total labeling and coloring of some bipartite graphs

The graph lattice in topological coding is a new encryption technology, like lattice base encryption. The graphs in a graph lattice are stored by matrices and run in a computer. The main theoretical techniques for topological coding come from mathematical disciplines such as discrete mathematics, number theory, and algebra. Because topological coding involves a large number of mathematical conjectures and NP problems, the numeric based strings generated by topological coding have irreversibility and computational security. In this paper, we have show some new labels and coloring, which are defined as follows: [Formula: see text]-module edge-difference total coloring, super [Formula: see text]-module edge-difference total coloring, set-ordered [Formula: see text]-module edge-difference total colorings and edge-difference [Formula: see text] total colorings. We have proven the graph obtained by three kinds of graph operations has the edge-difference type colorings and show the leaf adding algorithm. Our results can proved by algorithmic proofs.