Various Matchings of Graphic Groups For Graphic Lattices In Topological Coding

New security methods based on lattice cryptography emerge today. It has been shown that topological coding made by topological structures and mathematical restrictions can be used to serve information security, since the Number String Decomposition Problem of topological coding is NP-hard. We aim to producing topological coding, encrypting networks wholly and finding matching of twin graphic groups, multiple-graphic groups for serving the construction of graphic lattices. New coloring/labellings, matching-type graphic groups and infinite graphic groups will be discussed, a new Wait-filling Topcode-matrices Problem will be proposed.