The orientable genus of some joins of complete graphs with large edgeless graphs
The authors investigate the orientable genus of the join of a complete graph \(K_n\) with a large edgeless graph \(\overline{K_m}\). Concretely, they show that the genus of \(\overline{K_m}+K_n\) is equal to that of the complete bipartite graph \(K_{m,n}\) if \(n\) is even and \(m \geq n\). Also it is shown that the quality holds when \(n=2^p+2, p\geq 3\) and \(m\geq n-1\), or when \(n=2^p+1, p\geq 3\) and \(m\geq n+1\).
scientific article; zbMATH DE number 5542437
scientific article