Projects per year

## Abstract

© 2016 Australian Mathematical Publishing Association Inc.

We investigate properties which ensure that a given finite graph is the commuting graph of a group or semigroup. We show that all graphs on at least two vertices such that no vertex is adjacent to all other vertices is the commuting graph of some semigroup. Moreover, we obtain complete classifications of the graphs with an isolated vertex or edge that are the commuting graph of a group and the cycles that are the commuting graph of a centrefree semigroup.

We investigate properties which ensure that a given finite graph is the commuting graph of a group or semigroup. We show that all graphs on at least two vertices such that no vertex is adjacent to all other vertices is the commuting graph of some semigroup. Moreover, we obtain complete classifications of the graphs with an isolated vertex or edge that are the commuting graph of a group and the cycles that are the commuting graph of a centrefree semigroup.

Original language | English |
---|---|

Pages (from-to) | 335-355 |

Journal | Journal of the Australian Mathematical Society |

Volume | 101 |

Issue number | 3 |

Early online date | 13 May 2016 |

DOIs | |

Publication status | Published - Dec 2016 |

## Fingerprint Dive into the research topics of 'Realizability problem for commuting graphs'. Together they form a unique fingerprint.

## Projects

- 1 Finished