### Abstract

This paper explains the steps used to find the characteristic polynomial of the antiadjacency matrix of a cyclic dumbbell graph. The antiadjacency matrix of a graph is a matrix whose entries represent whether there is an edge that connects two vertices or not. The general form of the characteristic polynomial includes its eigenvalues. The antiadjacency matrix is obtained by using some theorems, the number of solutions of integer equations, quadratic formula, and polynomials factorization. Finally, results showed that the coefficients of the characteristic polynomial and its eigenvalues were dependent on the number of vertices of the cyclic dumbbell graph.

Original language | English |
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Article number | 012015 |

Journal | Journal of Physics: Conference Series |

Volume | 1108 |

Issue number | 1 |

DOIs | |

Publication status | Published - 4 Dec 2018 |

Event | 2nd Mathematics, Informatics, Science and Education International Conference, MISEIC 2018 - Surabaya, Indonesia Duration: 21 Jul 2018 → … |

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## Cite this

*Journal of Physics: Conference Series*,

*1108*(1), [012015]. https://doi.org/10.1088/1742-6596/1108/1/012015