dc.contributor.author | Badawi, Ayman | |

dc.contributor.author | El-Ashi, Yasmine Ahmed | |

dc.date.accessioned | 2022-12-07T07:48:45Z | |

dc.date.available | 2022-12-07T07:48:45Z | |

dc.date.issued | 2022-12-01 | |

dc.identifier.citation | Badawi, A., El-Ashi, Y. (2022). Graph of Linear Transformations Over R. In: Ashraf, M., Ali, A., De Filippis, V. (eds) Algebra and Related Topics with Applications. ICARTA 2019. Springer Proceedings in Mathematics & Statistics, vol 392. Springer, Singapore. https://doi.org/10.1007/978-981-19-3898-6_31 | en_US |

dc.identifier.isbn | 9789811938986 | |

dc.identifier.uri | http://hdl.handle.net/11073/25087 | |

dc.description.abstract | In this paper, we study a connection between graph theory and linear transformations of finite dimensional vector spaces over R (the set of all real numbers). Let Rm, Rn be finite vector spaces over R, and let L be the set of all non-trivial linear transformations from Rm into Rn. An equivalence relation ∼ is defined on L such that two elements f, k ∈ L are equivalent, f ∼ k, if and only if ker (f ) = ker (k). Let m, n ≥ 1 be positive integers and Vm,n be the set of all equivalence classes of ∼. We define a new graph, Gm,n, to be the undirected graph with vertex set equals to Vm,n, such that two vertices, [x] , [y] ∈ Vm,n are adjacent if and only if ker (x) ∩ ker (y) 6 = 0. The relationship between the connectivity of the graph Gm,n and the values of m and n has been investigated. We determine the values of m and n so that Gm,n is a complete graph. Also, we determine the diameter and the girth of Gm,n. | en_US |

dc.language.iso | en_US | en_US |

dc.publisher | Springer | en_US |

dc.relation.uri | https://doi.org/10.1007/978-981-19-3898-6_31 | en_US |

dc.subject | Zero-divisor graph | en_US |

dc.subject | Total graph | en_US |

dc.subject | Unitary graph | en_US |

dc.subject | Dot product graph | en_US |

dc.subject | Annihilator graph | en_US |

dc.subject | Linear transformations graph | en_US |

dc.title | Graph of Linear Transformations Over R | en_US |

dc.type | Book chapter | en_US |

dc.type | Postprint | en_US |

dc.identifier.doi | 10.1007/978-981-19-3898-6_31 | |