Total embedding distributions for bouquets of circles Original Research Article

Crosscap-number distributions, the distribution of graph embeddings into nonorientable surfaces, have been known for only a few cases. Chen et al. (Discrete Math. 128 (1994) 73) calculated the crosscap-number distribution of necklaces, closed-end ladders and cobblestone paths. In this paper, we compute the total genus polynomials and the total embedding polynomials of bouquets of circles with an aid of edge-attaching surgery technique. It extends their genus distributions computed by Gross et al. (J. Combin. Theory (B) 47 (1989) 292). The same work is also done for dipoles.