### Abstract

Using relatively elementary analysis in linear algebra, the authors establish some general results to estimate the expanding coefficients of bipartite graphs whose edges are defined by a finite number of some affine transformations. They prove that the constant delta of a bipartite graph is bounded below by 1 - lambda //2, where lambda //2 is the second largest eigenvalue of the matrix determined by affine transformations to specify the bipartite graph. Using these results, they can estimate the expanding coefficients of not only O. Grabber and Z. Galil's bipartite graphs but also some other graphs with good properties.

Original language | English |
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Title of host publication | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |

Publisher | ACM (Order n 508850) |

Pages | 88-97 |

Number of pages | 10 |

ISBN (Print) | 0897911512, 9780897911511 |

DOIs | |

Publication status | Published - Jan 1 1985 |

Externally published | Yes |

### Publication series

Name | Conference Proceedings of the Annual ACM Symposium on Theory of Computing |
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ISSN (Print) | 0734-9025 |

### ASJC Scopus subject areas

- Software

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## Cite this

Jimbo, S., & Maruoka, A. (1985). EXPANDERS OBTAINED FROM AFFINE TRANSFORMATIONS. In

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing*(pp. 88-97). (Conference Proceedings of the Annual ACM Symposium on Theory of Computing). ACM (Order n 508850). https://doi.org/10.1145/22145.22155