Properties of anti-adjacency matrix of directed cyclic sun graph

3rd Indonesian Operations Research Association - International Conference on Operations Research 2018

计算机科学

Prayitno, M.I.A.^1 ; Utama, S.^1 ; Aminah, S.^1

Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Depok, Jawa Barat

16424, Indonesia^1

关键词: Acyclic graphs;    Adjacency matrices;    Characteristic polynomials;    Cyclic graph;    Eigenvalues;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/567/1/012020/pdf
DOI  :  10.1088/1757-899X/567/1/012020

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

In this paper we focus on the properties of anti-adjacency matrix of directed cyclic sun graph. Some of these properties are related to the characteristic polynomials and the eigenvalues of the anti-adjacency of its matrix. We will show the general form of characteristic polynomial of the anti-adjacency matrix of directed cyclic sun graph by figuring out the number of the directed induced-cyclic graphs and the directed induced-acyclic graphs. After we find out the general form of the characteristic polynomial, we can find the general form of the eigenvalues of its polynomial by using factorization and Horner methods.