| Introduce to the concepts of the star total coloring, Smarandachely adjacentvertex star edge coloring and Smarandachely adjacent vertex acyclic edge coloring,and obtain some upper bounds of these chromatic numbers by the Lova′sz generalLocal lemma, respectively.Some preliminaries, such as basic concepts, lemmas and theorems which areincident to probabilistic method are given in the frst part;The star total coloring of graphs are discussed, and the star total chromatic num-bers of some subdivision graphs and maximal outer plane graphs, for instance, theS（Cn）ã€S(Wn+1)ã€S(Fn+1) and O4are given by using of the method of constructingconcrete coloring. And an upper bound for the star total chromatic number of agraph is obtained by probabilistic method in the second part;The concept of Smarandachely adjacent vertex star edge coloring of graphs isintroduced, and the Smarandachely adjacent vertex star edge chromatic numbersof some simple graphs, the cycle Cn, the fan Fnand the wheel Wnare given byusing of the method of constructing concrete coloring. An upper bound for theSmarandachely adjacent vertex star edge chromatic number of graphs is given byprobabilistic method in the third part;The concept of Smarandachely adjacent vertex acyclic edge coloring of graphsis considered. And an upper bound for the Smarandachely adjacent vertex acyclicedge chromatic number of a graph is obtained by probabilistic method in the fourthpart. |
