dc.contributor.advisor | Badawi, Ayman | |

dc.contributor.author | Abdulla, Mohammad Ahmad | |

dc.date.accessioned | 2016-05-11T09:06:40Z | |

dc.date.available | 2016-05-11T09:06:40Z | |

dc.date.issued | 2016-01 | |

dc.identifier.other | 29.232-2016.02 | |

dc.identifier.uri | http://hdl.handle.net/11073/8319 | |

dc.description | A Master of Science thesis in Mathematics by Mohammad Ahmad Abdulla entitled, "On The Unit Dot Product Graph Of A Commutative Ring," submitted in January 2016. Thesis advisor is Dr. Ayman Badawi. Soft and hard copy available. | en_US |

dc.description.abstract | In 2015, Ayman Badawi (Badawi, 2015) introduced the dot product graph associated to a commutative ring A. Let A be a commutative ring with nonzero identity, 1 n < 1 be an integer, and R =A x A x ... x A (n times). We recall from (Badawi, 2015) that total dot product graph of R is the (undirected) graph TD(R) with vertices R* = R \ {(0, 0, ..., 0)}, and two distinct vertices x and y are adjacent if and only if xy = 0 [is an element of] A (where xy denote the normal dot product of x and y). Let Z(R) denotes the set of all zero-divisors of R. Then the zero-divisor dot product graph of R is the induced subgraph ZD(R) of TD(R) with vertices Z(R) = Z(R)* \ {(0, 0, ..., 0)}. Let U(R) denotes the set of all units of R. Then the unit dot product graph of R is the induced subgraph UD(R) of TD(R) with vertices U(R). Let n 2 and A = Zn. The main goal of this thesis is to study the structure of UD(R = A x A). | en_US |

dc.description.sponsorship | College of Arts and Sciences | en_US |

dc.description.sponsorship | Department of Mathematics and Statistics | en_US |

dc.language.iso | en_US | en_US |

dc.relation.ispartofseries | Master of Science in Mathematics (MSMTH) | en_US |

dc.subject | Total dot product graphs | en_US |

dc.subject | zero dot product graphs | en_US |

dc.subject | dominating sets | en_US |

dc.subject | domination number | en_US |

dc.subject.lcsh | Commutative rings | en_US |

dc.title | On The Unit Dot Product Graph Of A Commutative Ring. | en_US |

dc.type | Thesis | en_US |