Graph Operations For Graphic Lattices and Graph Homomorphisms In Topological Cryptosystem

Abstract

We introduce graph operations: adding-removing edge or vertex operations, vertex-splitting and vertex-coinciding operations, edge-splitting and edge-coinciding operations, cycle-coinciding and cycle-splitting operations, H-coinciding and H-splitting operations, and so on. Next we build up graph operation lattices, self-isomorphic graph (anti-)homomorphisms, stochastic-graphic lattices and operation scale-free network lattices in topological coding. We show that our lattices introduced here possess the property like that of collision resistant hash functions.