Graph Theory Towards Module-K Odd-Elegant Labelling Of Graphical Passwords

Xiaohui Zhang,Hui Sun,Bing Yao,Bing Xu,Yinong Chen

doi:10.1051/matecconf/201713900206

Abstract

Graph labellings have been applied in many areas of science and engineering, such as in the development of redundant arrays of independent disks which incorporate redundancy utilizing erasure codes, algorithms, design of highly accurate optical gauging systems for use on automatic drilling machines, design of angular synchronization codes, design of optimal component layouts for certain circuit-board geometries, and determining configurations of simple resistor networks which can be used to supply any of a specified set of resistance values. Based on the idea of of “topological structure plus number theory” and magic type of various labellings for solving network transfer delay by using other type of graphical passwords. We define a new graph labelling, called Module-K odd-elegant labelling , and find some network models that admit our new labelling, and furthermore our methods can be transformed into effective algorithms.

Highlights

No report tells us that much of graphical passwords were applied to business and practice (Ref. [1], [2], [3])
An idea of “topological structure plus number theory” (Topsnut) as an alternative the existing graphical passwords is proposed in [6], which can be realized by graph labellings, and this idea is related with many mathematical conjectures, such as “Every tree is graceful” due to Rosa [4]
Odd-elegant labelling can induces some mathematical problems, such as: Every tree admits a Module-K odd-elegant labelling. We can plant this new labelling to other graph labellings, see [7], strongly graceful labelling in [10], odd-graceful labelling in [11], oddelegant labelling in [18], seven other labellings in [13] and so on, which mean that exploring new graphical passwords will bring more new mathematical subjects and new problems

Summary

Introduction

No report tells us that much of graphical passwords were applied to business and practice (Ref. [1], [2], [3]). K such that G admits a Module-K odd-elegant labelling. V1 } < min{ f (v) : v ∈ V2 }, we call f a set-ordered odd-elegant labelling, and write this case as f (V1 ) < f (V2 ).

Results

Conclusion