Smarandachely Adjacent Vertex Distinguishing E-total Coloring Of Some Graphs

The Smarandachely adjacent vertex distinguishing E-Total coloring of graph is an abnormal edge-total coloring such that no two adjacent vertices whose color sets have the relationship of subset each other,the minimum number of required colors is called the Smarandachely adjacent vertex distinguishing E-total coloring chromatic number.The paper mainly applies the methods of constructing function,structural anaysis to study Smarandachely adjacent vertex distinguishing E-total coloring of some join graphs,corona graphs,double graphs,complement double graphs,Mycielski’s graphs and generalized Myciel-ski’s graphs,and obtains their corresponding coloring numbers.Furthermore,it has been checked the conjecture of Smarandachely adjacent vertex distinguishing E-total coloring proposed by Prof.Zhang(2008).The paper is divided into four chapters:In the first chapter,we mainly introduce some basic concepts and symbols which will be used in the paper;In the second chapter,we consider Smarandachely adjacent vertex distinguishing E-total coloring of join graphs and corona graphs which axe constructed by some simple graphs such as path,cycle,star,fan,wheel and complete graph,and obtain their Smarandachely adjacent vertex distinguishing E-total chromatic number;In the third chapter,we study Smarandachely adjacent vertex distinguishing E-total color-ing of double graphs and complement double graphs which are constructed of some simple graphs such as path,cycle,star,fan,wheel,and their Smarandachely adjacent vertex distinguishing E-total chromatic number are obtained;In the fourth chapter,we consider Smaxandachely adjacent vertex distinguishing E-total coloring of Mycielski’s graphs and generalized Mycielski’s graphs which are constructed of some simple graphs such as path,cycle,star,fan,wheel,and obtain their Smarandachely adjacent vertex distinguishing E-total chromatic number,further verify the conjecture of Smarandachely adjacent vertex distinguishing E-total coloring is effective in the paper.