%A SHAN Song-ling;REN Han
%T Genus of C_{m,n} and strong genus embedding of K_{m,n}
%0 Journal Article
%D 2011
%J Journal of East China Normal University(Natural Science)
%R
%P 17-21
%V 2011
%N 2
%U {https://xblk.ecnu.edu.cn/CN/abstract/article_24563.shtml}
%8 2011-03-25
%X Let C_{m,n} be the join graph of C_{m}(a cycle of ength m) and n isolated vertices. In this paper, we first show hat the genus and nonorientable genus of C_{m,n} equal those of K_{m,n}, which were well known and discovered by Ringel [1, 2].

Then we show that the complete bipartite graph K_{m,n} has a strong orientable genus embedding if m≥2 and n≥2 and has a strong nonorientable genus embedding if m≥3 and n≥3.