Some Studies On The Endomorphisms Of Graphs

In this dissertation,we devote to study the endomorphism and the endomorphism types of double starlike tree and the lexicographic product of two bipartite graphs with an orthodox (regular) endomorphism monoid.There are three chapters in this paper.The first chapter introduces the study background and the basic notation.In chapter 2,we characterize the endomorphisms types of the connected graph double starlike tree and give the concrete number of its different endomorphisms.In chapter 3,the lexicographic of two graphs with an orthodox endomorphism monoid and a regular endomorphism monoid are dicussed,sufficient and necessary conditions of the lexicographic product of two bipartite graphs with an orthodox endomorphism monoid and a regular endomorphism monoid are given.