TY - JOUR

T1 - Characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic flower vase graph

AU - Aji, Bayu H.

AU - Sugeng, Kiki A.

AU - Aminah, Siti

N1 - Funding Information:
This research is funded by Hibah PUTI Prosiding Universitas Indonesia 2020 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 - This research discussed the characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic flower vase graph. The entries of the antiadjacency matrix of a directed graph represent the presence or the absence of a directed arc from one vertex to the others. If A is the adjacency matrix of a graph G→, then the antiadjacency matrix B of graph G→ is B = J − A, where J is the square matrix with all entries equal to one. The general form of characteristic polynomial coefficients of the antiadjacency matrix of directed unicyclic flower vase graph can be obtained by calculating the sum of determinants of the antiadjacency matrices of all induced cyclic and acyclic subgraphs, while the eigenvalues were obtained by using polynomial factorization and Horner's method. This paper gives the characteristic polynomial coefficients and eigenvalues of antiadjacency matrix of directed unicyclic flower vase graph. The characteristic polynomial can be considered as a function that depends on the number of vertices.

AB - This research discussed the characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic flower vase graph. The entries of the antiadjacency matrix of a directed graph represent the presence or the absence of a directed arc from one vertex to the others. If A is the adjacency matrix of a graph G→, then the antiadjacency matrix B of graph G→ is B = J − A, where J is the square matrix with all entries equal to one. The general form of characteristic polynomial coefficients of the antiadjacency matrix of directed unicyclic flower vase graph can be obtained by calculating the sum of determinants of the antiadjacency matrices of all induced cyclic and acyclic subgraphs, while the eigenvalues were obtained by using polynomial factorization and Horner's method. This paper gives the characteristic polynomial coefficients and eigenvalues of antiadjacency matrix of directed unicyclic flower vase graph. The characteristic polynomial can be considered as a function that depends on the number of vertices.

UR - http://www.scopus.com/inward/record.url?scp=85100738514&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1722/1/012055

DO - 10.1088/1742-6596/1722/1/012055

M3 - Conference article

AN - SCOPUS:85100738514

VL - 1722

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012055

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

Y2 - 12 October 2020 through 15 October 2020

ER -