On The Determination Of The Genus Distributions Of Graphs

This paper mainly studies genus distributions of graphs in orientable surfaces, which belongs to the embedding theory of counting. Mainly used to solve some prob-lems about the scope of genus of an embedded surface for a graph and different embed-ding numbers in a surface.And using the joint trees theory proposed by professor Liu Yanpei and other recursive polynomials to get some explicit formulations in small genus and large genus, as well as some simple recursion formulations so that the embedding numbers can be computed more easily.In chapter1:we gives some definitions,lemmas,theorem and research background about graph embedding on orientable surfaces,further more, we describes joint tree model in detail and introduces the structure and content of each chapter of this paper.In chapter2:we summarizes some recent conclusions of orientable genus embed-ding distributions ofK1,3ladders graph Vn And further optimizes its result.In chapter3:we obtain the orientable genus embedding distributions of a new kind of graph called K1,4ladders Wn on the bases of joint trees of a graph proposed by Professor Liu,and through the further recurrence and reduction,we get the explicit formulation of the embedding distributions of Wn in the smaller numbers of genera,and the simple recursive relation in other genera,so that its number of orientable embedding distributions can be easily obtained.In chapter4:we depicts the orientable genus embedding distributions of a kind of3-regular graph called kite graph Fn, and concludes the optimization results.