Open AccessProperties of anti-adjacency matrix of directed cyclic sun graph
Author(s) -
Muhammad Irfan Arsyad Prayitno,
Suarsih Utama,
Siti Aminah
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/567/1/012020
Subject(s) - adjacency matrix , graph energy , adjacency list , combinatorics , mathematics , degree matrix , characteristic polynomial , eigenvalues and eigenvectors , directed graph , polynomial matrix , matrix polynomial , two graph , discrete mathematics , graph , polynomial , line graph , graph power , physics , mathematical analysis , quantum mechanics
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.