Some Cryptography Models Designed by Double Odd-Edge Labelling of Trees

Cryptography has been around for thousands of years. We propose a new cryptographic model, lock trees and key trees, and our idea differs from current graphical passwords in this paper. Graphs and their labellings are applied to establish the concepts of key-trees and lock-trees based on abundant of graphs having smaller orders and their corresponding double odd-edge labellings. We propose two methods, called Edge-Construction and Paste-Construction-w, to construct trees of larger orders by some smaller trees such that the new trees have some DOElabellings. Our results may be valued to information security and graph theory, at the end of this article we propose several conjectures.