Misalkan G(V(G),E(G)) adalah suatu graf dengan V(G) yang merupakan himpunan simpul tak kosong dan E(G) yang merupakan himpunan busur. Jika B adalah matriks antiadjacency dari graf berarah G ⃗, maka dapat dibentuk suatu polinomial karakteristik det⁡〖(λI-B((G)) ⃗)〗. Sifat-sifat polinomial karakteristik matriks antiadjacency dari graf berarah asiklik sudah dibahas, akan tetapi sifat untuk graf berarah yang memuat subgraf lingkaran belum diketahui. Pada skripsi ini diberikan sifat-sifat polinomial karakteristik matriks antiadjacency dari graf berarah siklik, khususnya graf lingkaran berarah (C_n ) ⃗ dan graf lingkaran berarah dengan penambahan satu chord (C_n^t ) ⃗.

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Let G(V(G),E(G)) be a graph with V(G) which is a nonempty set of vertices and E(G) which is a set of arcs. If B is an antiadjacency matrix of a directed graph G ⃗, then its characteristic polynomial det⁡〖(λI-B((G)) ⃗)〗. The properties of the characteristic polynomial of antiadjacency matrix of acyclic directed graph has been discussed. However, the properties of the directed graph contains a circle subgraph is unknown. In this thesis the properties of antiadjacency matrix characteristic polynomial of a cyclic directed graph is given, specifically for directed cycle graph (C_n ) ⃗ and directed cycle graph with the addition of one chord (C_n^t ) ⃗.