The Rainbow Connected Numbers Of Some Special Digraphs

The famous Konigsberg Bridge Problem is the origin of graph theory problem,then graph theory has become an important branch of applied mathematics research.The rainbow connection has application in transferring information of high security in multicomputer net-works,in recent years,with the rapid development of information technology,the coloring of graphs has gradually become a hot issue in research of graph theory.Connectivity is one of the basic properties in graph theory,there are many ways to strengthen connectivity,such as hamiltonian,k-connectivity^[1].Rainbow connectivity can also be regarded as a general connectivity enhancement.In 2008,chartrand^[2]and et al firstly introduced and studied the rainbow connectivi-ty of graphs,and determined the number of rainbow connection of some special graphs.Chakraborty^[3]et al proved that calculating the rainbow connected number of general graph is a N P-difficult problem.So it is very meaningful to determine the number of rainbow connections for some special graphs.This paper focuses on the rainbow connectivity of digraphs,all contents consist of four chapters,and the concrete content and research results are as follows:In chapter 1,we firstly introduce some background and development status of the rain-bow connection^[4],then give some basic concepts,terms and symbols used in this paper,and finally enumerate the main results of this paper.In chapter 2,give the explicit value of the rainbow connected numbers of some special digraphs and their mycielskian graphs.In chapter 3,give the upper bound of the rainbow connected numbers of mycielskian graphs of simple digraphs and their generalized mycielskian graphs.In chapter 4,give the explicit value of the rainbow connected numbers of the symmetric digraphs of star of generalized mycielskian graphs.