Suatu graf berarah sederhana , dengan simpul dan busur dapat direpresentasikan dalam bentuk matriks antiadjacency, yaitu matriks , dengan adalah matriks adjacency dari graf berarah sederhana dan adalah matriks yang berukuran , dengan semua entrinya bernilai 1. Pada tesis ini diberikan beberapa sifat nilai eigen matriks antiadjacency dari graf berarah sederhana dan sifat nilai eigen pada beberapa kelas graf berarah sederhana, yaitu graf bipartit lengkap berarah, graf lintasan lengkap berarah, graf lingkaran berarah, graf korona berarah dan graf lengkap berarah.

---

A simple graph , with vertices and edges can be represented as an antiadjacency matrix , where is an adjacency matrix of a simple directed graph and is an matrix, with all of the entries are 1. In this thesis, a study on some properties of the eigenvalues of the antiadjacency matrix of a simple directed graph as well as for some classes of simple directed graphs is carried out. The classes of simple directed graphs being explored are complete bipartite directed graphs, complete path directed graphs, cycle directed graphs, corona directed graphs and complete directed graphs.