Smarandachely Adjacent Vertex Ⅰ-Total Coloring On Several Kinds Of Graphs

Let G be a finite and undirected simple graph with vertex set V and edge set E.A Smarandachely adjacent vertex distinguishing Ⅰ-total coloring of graph is an edge-abnormal total coloring such that no two adjacent vertices has the relation of subset between its color sets,the minimal number of the required colors in the coloring is called Smarandachely adjacent vertex distinguishing Ⅰ-total chromatic number.In this paper,according to the structural properties of graphs,we consider the Smarandachely adjacent vertex distinguishing Ⅰ-total coloring of several simple graphs and its double graphs,corona graphs and Mycielski’s graphs by the structural patchwork method,the constructed coloring function method and the exhaustion method.The paper is divided into five chapter:In the first chapter,we introduce some fundamental concepts and symbols which will be used throughout this paper.In the second chapter,we study the Smarandachely adjacent vertex distinguishing Ⅰ-total coloring question of several simple graphs,and give their corresponding chromatic numbers.In the third chapter,we discuss the Smarandachely adjacent vertex distinguishing Ⅰ-total coloring of some double graphs,and give their corresponding chromatic numbers.In the fourth chapter,we study the Smarandachely adjacent vertex distinguishing Ⅰ-total coloring of some corona graphs,and give their corresponding chromatic numbers.In the fifth chapter,we study the Smarandachely adjacent vertex distinguishing Ⅰ-total coloring question of some Mycielski’s graphs,and give their corresponding chromatic number.