On the basis of lit.\([9]\), by the joint tree model, the lower bound of the number of genus embeddings for complete tripartite graph \(K_{n,n,\ell}\) \((\ell \geq m \geq 1)\) is got.
Citation
Zeling Shao, Yanpei Liu. On the Number of Genus Embeddings of Complete Tripartite Graph \(K_{n,n,1}\)[J], Ars Combinatoria, Volume 104. 129-142. .