New Labellings Based on the Idea of Graphical Construction Plus Number Theory for Designing Cryptographs

Abstract

Based on the thought of new password design of “graphical construction plus number theory†as well as the edge magic graceful labelling, we defined a new graph labelling called (ki) 1 m -edge magic graceful totally labelling (m2), and obtain the properties of these two labellings on graphs. We show several new algorithms for constructing graphs having these two labellings, and furthermore show that every graph admits at least a (ki) 1 m -edge magic graceful totally labelling.