TY - JOUR

T1 - Properties of characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic helm graph

AU - Okfradifa, Rizky P.

AU - Aminah, Siti

AU - Sugeng, Kiki A.

N1 - Funding Information:
This research is funded by Hibah PUTI Prosiding Universitas Indonesia 2020 No. 1008/UN2.RST/HKP.05.00/2020.
Publisher Copyright:
© 2021 Institute of Physics Publishing. All rights reserved.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/1/7

Y1 - 2021/1/7

N2 - A directed unicyclic graph is a directed graph that has only one directed cycle subgraph. A directed unicyclic helm graph H-n is obtained from a directed wheel graph W-n by adjoining a directed pendant edge at each vertex of the cycle. A directed graph can be represented into several matrix representations, one of them is the antiadjacency matrix. The antiadjacency matrix is a matrix in which the entries represent whether there is a directed edge from one vertex to another. This paper discusses the general form of the coefficients of the characteristic polynomial that obtained by adding all of the determinants of antiadjacency matrix from each induced acyclic and cyclic subgraphs. The eigenvalues of the antiadjacency matrix of the directed unicyclic helm graph obtained by polynomial factorization. The result obtained denotes that the coefficients of the characteristic polynomial and eigenvalues of the antiadjacency matrix depend on the number of vertices of the cycle subgraphs of directed unicyclic helm graph.

AB - A directed unicyclic graph is a directed graph that has only one directed cycle subgraph. A directed unicyclic helm graph H-n is obtained from a directed wheel graph W-n by adjoining a directed pendant edge at each vertex of the cycle. A directed graph can be represented into several matrix representations, one of them is the antiadjacency matrix. The antiadjacency matrix is a matrix in which the entries represent whether there is a directed edge from one vertex to another. This paper discusses the general form of the coefficients of the characteristic polynomial that obtained by adding all of the determinants of antiadjacency matrix from each induced acyclic and cyclic subgraphs. The eigenvalues of the antiadjacency matrix of the directed unicyclic helm graph obtained by polynomial factorization. The result obtained denotes that the coefficients of the characteristic polynomial and eigenvalues of the antiadjacency matrix depend on the number of vertices of the cycle subgraphs of directed unicyclic helm graph.

UR - http://www.scopus.com/inward/record.url?scp=85100742586&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1722/1/012056

DO - 10.1088/1742-6596/1722/1/012056

M3 - Conference article

AN - SCOPUS:85100742586

SN - 1742-6588

VL - 1722

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012056

T2 - 10th International Conference and Workshop on High Dimensional Data Analysis, ICW-HDDA 2020

Y2 - 12 October 2020 through 15 October 2020

ER -