### Abstract

An adjacency matrix A(G) of directed graph G is an m×m matrix consisting of only entries 0 and 1, where m is the number of vertices of G. The entry a_{ij} is equal to 1 if there exists a directed edge from vertex v_{i} to vertex v_{j}, otherwise it is equal to 0. Let D(G) be a diagonal matrix of size m×m with each of its main diagonal entry being the degree of the corresponding vertex of directed graph G. Then the matrix L(G) = D(G) - A(G) is called the Laplacian matrix of G. Since a directed graph has two types of degrees namely indegree and outdegree, they result in directed graphs also having the both types of its Laplacian matrices. In this study, the adjacency matrix and the Laplacian matrix of cyclic directed prism graph are investigated. The general form of the coefficients of polynomial characteristic of the Adjacency matrix and Laplacian matrix, respectively is obtained by applying the row reduction method in linear algebra, whereas the general form of the eigenvalues of the polynomial characteristic of the Adjacency matrix and Laplacian matrix, respectively is obtained by factorization and substitution methods.

Original language | English |
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Title of host publication | Proceedings of the 5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019 |

Editors | Terry Mart, Djoko Triyono, Tribidasari Anggraningrum Ivandini |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735420014 |

DOIs | |

Publication status | Published - 1 Jun 2020 |

Event | 5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019 - Depok, Indonesia Duration: 9 Jul 2019 → 10 Jul 2019 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 2242 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | 5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019 |
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Country | Indonesia |

City | Depok |

Period | 9/07/19 → 10/07/19 |

### Keywords

- Adjacency matrix
- cyclic directed graph
- indegree Laplacian matrix
- outdegree Laplacian matrix
- prism graph

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## Cite this

*Proceedings of the 5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019*[030028] (AIP Conference Proceedings; Vol. 2242). American Institute of Physics Inc.. https://doi.org/10.1063/5.0008300