### 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 |
---|---|

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 |

Publication status | Published - 1985 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Software

### Cite this

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing*(pp. 88-97). ACM (Order n 508850).

**EXPANDERS OBTAINED FROM AFFINE TRANSFORMATIONS.** / Jinbo, Shuji; Maruoka, Akira.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Conference Proceedings of the Annual ACM Symposium on Theory of Computing.*ACM (Order n 508850), pp. 88-97.

}

TY - GEN

T1 - EXPANDERS OBTAINED FROM AFFINE TRANSFORMATIONS.

AU - Jinbo, Shuji

AU - Maruoka, Akira

PY - 1985

Y1 - 1985

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0021901601&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021901601&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0021901601

SN - 0897911512

SP - 88

EP - 97

BT - Conference Proceedings of the Annual ACM Symposium on Theory of Computing

PB - ACM (Order n 508850)

ER -