Research On Some Graph Labeling Problems

Graph theory is a branch of mathematics,especially an important branch of discrete mathematics.It has been applied in many different fields in the modem world,such as physics,chemistry,astronomy,geography,biology,as well as in computer science and engineering.This dissertation mainly researches on graph labeling.Graph labeling traces its origin to the famous conjecture that all trees are graceful presented by A.Rosa in 1966.Vertex labeling is a mapping that maps the vertex set into integer set(in general into an Abelian group).On the other hand, edge labeling maps edge set into integer set.According to the different requirement for the mapping,many variations of graph labelings have been evolved.This article introduced the graceful labelings on graph C_n^t by the method of the enumeration law and mathematics inference;researched on the irregular total labeling and two(a,d)- super anti magic total labelings,and solved some problems and the conjecture.Graceful labeling serves as useful models for a broad range of applications such as astronomy and communication networks.In this paper introduced the graceful of graph C_n^t when n = 7,9,11 and for any positive integer t,and proved that Koh's conjecture is true.In 2007,the irregular total labeling was introduced by Baca,et al.,and gave the conjecture about the total edge irregularity strength of complete graph,in this paper the conjecture was proved out and gave the general result on any kind of graph G.Magic labeling is motivated from magic squares in number theory. (a,d)- super edge anti magic total labeling is one of magic labeling with more strict limits,and is related with other well-known classes of labelings.In this paper researched on the graph mK,and graph mQ_n about(a,d)-super edge anti magic total labeling,and gave result about a,d.