The Key-models And Their Lock-models For Designing New Labellings Of Networks
Hongyu Wang, Xu Jin, Bing Yao · Scientia Forestalis · 2016
The security of real networks is facing serious challenges and is harder than ever. We propose an idea of “topological structure + number theory” for designing new passwords. By means of graph theory we define a twin odd-graceful tree T = T 1 ○ T 2 obtained by identifying a certain vertex of T 1 with a certain vertex of T 2 together. We prove that some particular trees (key-models) can have their associated trees (lock-models) under the concept of twin odd-graceful trees. Trees having set-ordered odd-graceful labellings T 1 with their associated trees T 2 can produce certain twin odd-graceful trees such that these twin odd-graceful trees are odd-graceful.