Matrices From Topological Graphic Coding of Network Security

Abstract

Matrices as mathematical models have been used in each branch of scientific fields for hundred years. We propose a new type of matrices, called topological coding matrices (Topcode-matrices). Topcode-matrices show us the following advantages: Topcode-matrices can be saved in computer easily and run quickly in computation; since a Topcode-matrix corresponds two or more Topsnut-gpws, so Topcode-matrices can be used to encrypt networks such that the encrypted networks have higher security; Topcode-matrices can be investigated and applied by people worked in more domains; Topcode-matrices can help us to form new operations, new parameters and new topics of graph theory, such as vertex/edge splitting operations and connectivities of graphs. Several properties and applications on Topcode-matrices, and particular Topcode-matrices, as well as unknown problems are introduced.