TY - JOUR

T1 - Characteristic polynomial and eigenvalues of anti-adjacency matrix of directed unicyclic corona graph

AU - Hasyyati, N.

AU - Sugeng, K. A.

AU - Aminah, S.

N1 - Publisher Copyright:
© 2021 Published under licence by IOP Publishing Ltd.

PY - 2021/3/23

Y1 - 2021/3/23

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85103580967&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1836/1/012001

DO - 10.1088/1742-6596/1836/1/012001

M3 - Conference article

AN - SCOPUS:85103580967

SN - 1742-6588

VL - 1836

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012001

T2 - 4th International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2020

Y2 - 22 August 2020 through 23 August 2020

ER -