Graph Colorings and Labelings Having Multiple Restrictive Conditions in Topological Coding

Abstract

With the fast development of networks, one has to focus on the security of information running in real networks. A technology that might be able to resist attacks equipped with AI techniques and quantum computers is the so-called topological graphic password of topological coding. In order to further study topological coding, we use the multiple constraints of graph colorings and labelings to propose 6C-labeling, 6C-complementary labeling, and its reciprocal-inverse labeling, since they can be applied to build up topological coding. We show some connections between 6C-labeling and other graph labelings/colorings and show graphs admitting twin-type 6C-labelings, as well as the construction of graphs admitting twin-type 6C-labelings.