## Abstract

To calculate the genus polynomials for a recursively specifiable sequence of graphs, the set of cellular imbeddings in oriented surfaces for each of the graphs is usually partitioned into imbedding-types. The effects of a recursively applied graph operation τ on each imbedding-type are represented by a production matrix. When the operation τ amounts to constructing the next member of the sequence by attaching a copy of a fixed graph H to the previous member, Stahl called the resulting sequence of graphs an H-linear family. We demonstrate herein how representing the imbedding types by strings and the operation τ by string operations enables us to automate the calculation of the production matrices, a task requiring time proportional to the square of the number of imbedding-types.

Original language | English |
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Pages (from-to) | 267-295 |

Number of pages | 29 |

Journal | Ars Mathematica Contemporanea |

Volume | 15 |

Issue number | 2 |

DOIs | |

State | Published - 2018 |

### Bibliographical note

Publisher Copyright:© 2018 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.

## Keywords

- Genus polynomial
- Graph imbedding
- Production matrix
- Transfer matrix method

## ASJC Scopus subject areas

- Theoretical Computer Science
- Algebra and Number Theory
- Geometry and Topology
- Discrete Mathematics and Combinatorics