Overlap matrices and total imbedding distributions
For a given graph \(G\), let \(\alpha_ g(G)\), \(g= 0,1,2,\dots\), denote the number of homeomorphically different 2-cell embeddings of \(G\) in a surface of genus \(g\). The sequence \(\alpha_ g(G)\), \(g=0,1,2,\dots\), is the genus distribution of \(G\). This concept can be extended to include nonorientable embeddings. The authors determine the extended embedding distributions for several classes of graphs. The computations in the nonorientable case are done by applying a theorem of the reviewer [An obstruction to embedding graphs in surfaces, Discrete Math. 78, No. 1/2, 135-142 (1989; Zbl 0686.05019)] that relates the topological types of embedding surfaces to ranks of the corresponding overlap matrices.
scientific article; zbMATH DE number 562584
scientific article