### Abstract

A prism graph is a graph which corresponds to the skeleton of an n-prism and therefore it is a cyclic simple graph. It is denoted Y_{n} (n ≥ 3) where n is half the number of vertices. An n-prism graph has 2n vertices and 3n edges. In this paper, only regularly-directed cyclic prism graphs are investigated. The anti-adjacency matrix is applied as the graph representation. An anti-adjacency matrix of graph representation is a 0-1 matrix of size m × m where m is the number of vertices. The entry b_{ij} of an anti-adjacency matrix B(G) of directed graph G is 0 if there exists a directed edge from vertex v_{i} to vertex v_{j} and is 1 otherwise. The characteristic polynomial of the anti-adjacency matrix B(Y_{n}) of directed cyclic prism graph Y_{n} are obtained. The characteristic polynomial will be proved by observing the both cyclic and acyclic induced subgraphs of the directed cyclic prims graph. Furthermore, the anti-adjacency matrix of directed cyclic prism graph is found to have both real eigenvalues and complex eigenvalues which appear in conjugate pairs.

Original language | English |
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Title of host publication | Proceedings of the 4th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2018 |

Editors | Terry Mart, Djoko Triyono, Ivandini T. Anggraningrum |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735419155 |

DOIs | |

Publication status | Published - 4 Nov 2019 |

Event | 4th International Symposium on Current Progress in Mathematics and Sciences 2018, ISCPMS 2018 - Depok, Indonesia Duration: 30 Oct 2018 → 31 Oct 2018 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 2168 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | 4th International Symposium on Current Progress in Mathematics and Sciences 2018, ISCPMS 2018 |
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Country | Indonesia |

City | Depok |

Period | 30/10/18 → 31/10/18 |

### Keywords

- Anti-adjacency matrix
- characteristic polynomial
- directed graph
- eigenvalues
- prism graph

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## Cite this

*Proceedings of the 4th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2018*[020052] (AIP Conference Proceedings; Vol. 2168). American Institute of Physics Inc.. https://doi.org/10.1063/1.5132479