Research on Some Selected Graph Labeling Topics in Graph Theory.pdf

1、Graph labeling is a relatively young 5nab-field of graph theory，The first bona fidegraph labeling problem is the bandwidth problem,which is concerned with minhnizingthe difference between the labels of adjacent vertices.

2、Bandwidth was originally,studiedin the 1950's.in relation to matrices with all non-zero elements lying within a narrwband about the main diagonal.In 1966 A.Rosa introduced the famous conjecture thatall trees are graceful

3、 with a new type of graph labeling“Graceful labeling”.In this thesis，combining the computer constructive prove with mathematical prove，soine classes of graph labelings：Prime cordial labeling and Prime labeling Die resear

4、ched. Many nmnber puzzles involve prime numbers.Prime numbering or prime labeling is motivated kom Magic matrix，A graph is called prime if it has a prilzle labeling.This concept was originated with Entringer and intr

5、oduced by Tout，Dabboucy,and Howalla.In 1980 Entringer conjectured that all trees are prime.From recent reFr朗.rch we knowthat following graphs are prime：every tree with n≤50，disjoint union of C<,2K> and Cn，F(xiàn)ans，Helms，F(xiàn)low

6、ers，Stars，K<,2n> and K<,3n> unless n=3 or 7.In this thesis，we provethat following graphs axe prime：generalized Petersen graphs P(n,1)n≤2500) and P(n,3)(n≤100) for even n Knodel graph w<,3n>(n≤130) and Mobjus ladder Mn(5≤