Total embedding distributions for bouquets of circles

Authors:
Jin Ho Kwak;Sang Ho Shim
Affiliations:
Pohang University of Science and Technology, Department of Mathematics, San 31 Hyoja Dong, Pohang 790-784, South Korea;Pohang University of Science and Technology, Department of Mathematics, San 31 Hyoja Dong, Pohang 790-784, South Korea
Venue:
Discrete Mathematics
Year:
2002

Citing 6
Cited 1

Topological graph theory

Topological graph theory
Genus distributions for two classes of graphs

Journal of Combinatorial Theory Series B
Genus distributions for bouquets of circles

Journal of Combinatorial Theory Series B
An obstruction to embedding graphs in surfaces

Discrete Mathematics - In memory of Tory Parsons
Overlap matrices and total imbedding distributions

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Enumeration of graph embeddings

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Orientable embedding genus distribution for certain types of graphs

Journal of Combinatorial Theory Series B

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Abstract

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.