摘要
The embedding technique based on an operator appeared in [Liu, Y. P., Scientia Sinica, Special Issue on Math,1 (1979),191-201 (in Chinese)] for determining the maximum non-orientable genus of a graph is developed to obtain the general theorem which presents a necessary and sufficient condition for a graph to be embeddable into either the orientable or the non-orientable surface of genus k. Furthermore,the greatest lower bound of the lengths of genus ranges of the class of nonplanar graphs which are up-embeddable is also obtained.
