Researching Graph Labellings On Some Growing Network Models

The random network theory was first proposed by Erdos and Ranyi.The random network can describe many complex systems in our life,and researchers investigate its problems appeared in application by theoritical methods.In recent years,researchers on the random network have done a lot of explorition and study,and have achieved many gains,which makes the research of stochastic network is rapid development.The network labellings,not only is an important topic in net-work research,and is a more active branch in mathematics.It can form a new-type of graphical password by topology structure plus number theory in cryptography,but also has important applications in communication network establishment,read DNA sequence and so on.This paper mainly do the following work:1?Present the definitions of graceful labeling,odd-graceful labeling,strongly(k,d)-graceful labeling.We create the so-called suspension-split operation,and con-struct super strongly graceful lobsters by strongly graceful trees,as well as study some properties of such lobsters.2?Using strongly(k,d)-graceful labelings discusses(k,d)-edge magic total la-bellings of graph theory;and using our method producees trees having(k,d)-edge magic total labellings by smaller scale of set-ordered(k,d)-graceful trees.Most im-portantly,we obtain some connections between set-ordered(k,d)-graceful labeling and(k,d)-edge magic total labeling on trees.3?Except using the so-called suspension-split operation in theoritical proof,we can transform easily it algorithm in orderto do computer test quickly and dffectively,and rpovide a basic in future application in practices.