### Abstract

We give new examples of graphs with the n-e.c. adjacency property. Few explicit families of n-e.c. graphs are known, despite the fact that almost all finite graphs are n-e.c. Our examples are collinearity graphs of certain partial planes derived from affine planes of even order. We use probabilistic and geometric techniques to construct new examples of n-e.c. graphs from partial planes for all n, and we use geometric techniques to give infinitely many new explicit examples if n = 3. We give a new construction, using switching, of an exponential number of non-isomorphic n-e.c. graphs for certain orders.

Original language | English |
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Pages (from-to) | 901-912 |

Number of pages | 12 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 5-6 |

DOIs | |

Publication status | Published - Mar 28 2008 |

### Keywords

- Adjacency property
- Affine plane
- Geometry
- Graph
- Switching
- n-e.c. graph

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics

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## Cite this

Baker, C. A., Bonato, A., Nowlin Brown, J. M., & Szonyi, T. (2008). Graphs with the n-e.c. adjacency property constructed from affine planes.

*Discrete Mathematics*,*308*(5-6), 901-912. https://doi.org/10.1016/j.disc.2007.07.029