Open AccessCharacteristic polynomial and eigenvalues of anti-adjacency matrix of directed unicyclic corona graph
Author(s) -
N Hasyyati,
Kiki Ariyanti Sugeng,
Siti Aminah
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1836/1/012001
Subject(s) - adjacency matrix , graph energy , combinatorics , mathematics , adjacency list , characteristic polynomial , eigenvalues and eigenvectors , discrete mathematics , degree matrix , directed graph , graph , polynomial , line graph , graph power , physics , mathematical analysis , quantum mechanics
A directed graph can be represented by several matrix representations, such as the anti-adjacency matrix. This paper discusses the general form of characteristic polynomial and eigenvaluesof the anti-adjacencymatrix of directed unicyclic corona graph. The characteristic polynomial of the anti-adjacency matrix can be found by counting the sum of the determinant of the anti-adjacency matrix of the directed cyclic inducedsubgraphs and the directed acyclic induced subgraphs from the graph. The eigenvalues of the anti-adjacency matrix can be real or complex numbers. We prove that the coefficient of the characteristic polynomial and the eigenvalues of the anti-adjacency matrix of directed unicyclic corona graph can be expressed in the function form that depends on the number of subgraphs contained in thedirected unicyclic corona graphs.