### Abstract

A directed graph can be represented by several matrix representations, such as adjacency matrix, in-degree Laplacian matrix, and out-degree Laplacian matrix. A directed cyclic sun graph is a directed graph which is obtained by adding a directed edge and a vertex called the outer vertex as its tail to every vertex in the directed cycle graph. The inner vertices always form a directed cycle graph. The directed edges in the cycle graph is oriented in such a away so that clockwise. In this paper we give the properties of adjacency, in-degree Laplacian, and out-degree Laplacian matrices of directed cyclic sun graph such as characteristic polynomial and eigenvalues. The eigenvalues of the matrices mentioned above can be real or complex numbers.

Original language | English |
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Title of host publication | Proceedings of the 8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019 |

Subtitle of host publication | Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations |

Editors | Herni Utami, Fajar Adi Kusumo, Nanang Susyanto, Yeni Susanti |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735419438 |

DOIs | |

Publication status | Published - 19 Dec 2019 |

Event | 8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations - Yogyakarta, Indonesia Duration: 29 Jul 2019 → 1 Aug 2019 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 2192 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | 8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations |
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Country | Indonesia |

City | Yogyakarta |

Period | 29/07/19 → 1/08/19 |

### Keywords

- adjacency matrix
- characteristic polynomials
- directed cyclic sun graph
- eigenvalues
- in-degree Laplacian matrix
- out-degree Laplacian matrix

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## Cite this

*Proceedings of the 8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations*[040011] (AIP Conference Proceedings; Vol. 2192). American Institute of Physics Inc.. https://doi.org/10.1063/1.5139137