Smarandachely Adjacent Vertex Distinguishing Coloring Of Graphs With Maximum Degree 3

As a new branch of mathematics,graph theory has a wide application in most fields and is taken seriously by the mathematical community and other scientific circles,although it exists only 200 year.In this paper,we mainly consider about the following problems:Smarandachely adjacent vertex distinguishing total coloring of the simple graph and the series parallel graph with maximum degree 3;Smarandachely adjacent vertex distinguishing edge coloring of the simple graph and the series parallel graph with maximum degree 3;A simple graph refers to an undirected finite graph that doesn't include multiple edges and loops.A graph is called series parallel graph if and only if its any subgraph not homeomorphic to K4.This paper is divided into four chapters.In chapter 1,we introduce graphical concepts,graphical definitions,such studies' development and its historical background.In chapter 2,we discuss the adjacent vertex distinguishing total coloring and edge coloring of graph.Combined with P.N.Balister method,we are easy to get the adjacent vertex distinguishing total chromatic number and edge chromatic number of generalized ?-graph.In chapter 3,we study the smarandachely adjacent vertex distinguishing total coloring,proving that the smarandachely adjacent vertex distinguishing total chromatic number of the series parallel graph with maximum degree 3 doesn't exceed 6 and the smarandachely adjacent vertex distinguishing total chromatic number of the simple graph with maximum degree 3 does not exceed 7.In chapter 4,we study the smarandachely adjacent vertex distinguishing edge coloring,proving that the smarandachely adjacent vertex distinguishing edge chromatic number of the series parallel graph with maximum degree 3 doesn't exceed 7 and the smarandachely adjacent vertex distinguishing edge chromatic number of the simple graph with maximum degree 3 doesn't exceed 8.