TY - JOUR

T1 - Characteristic polynomial of anti-Adjacency matrix of directed cyclic friendship graph

AU - Anzana, N.

AU - Aminah, S.

AU - Utama, S.

AU - Silaban, D. R.

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

PY - 2020/6/19

Y1 - 2020/6/19

N2 - Graph theory has some applications. One of them is used to do social network analysis as in Facebook with each person as nodes and every like, share, comment, tag as edges. Usually a network can be represented by a graph. Analysing a network is the same as analysing the structure of a graph. A structure of a graph can be analysed through some matrix representations such as anti-Adjacency matrix. The entries of the anti-Adjacency matrix of a directed graph represent the presence or absence of directed arcs from a vertex to the others. This paper is about the properties of the anti-Adjacency matrix of directed cyclic friendship graph, those are the characteristic polynomial and the eigenvalues of the anti-Adjacency matrix. The method used to obtain the general form of the coefficients of the characteristic polynomial is by adding up the determinant values of all directed induced subgraphs, cyclic or acyclic, of the directed cyclic friendship graph. Furthermore, the methods used to find theeigenvalues of the anti-Adjacency matrix of directed cyclic friendship graph are the substitution method and factorization method. The result of this researcharethe general form of the coefficients of the characteristic polynomial and the general form of the eigenvalues of the anti-Adjacency matrix depend on the number of triangles in directed cyclic friendship graph.

AB - Graph theory has some applications. One of them is used to do social network analysis as in Facebook with each person as nodes and every like, share, comment, tag as edges. Usually a network can be represented by a graph. Analysing a network is the same as analysing the structure of a graph. A structure of a graph can be analysed through some matrix representations such as anti-Adjacency matrix. The entries of the anti-Adjacency matrix of a directed graph represent the presence or absence of directed arcs from a vertex to the others. This paper is about the properties of the anti-Adjacency matrix of directed cyclic friendship graph, those are the characteristic polynomial and the eigenvalues of the anti-Adjacency matrix. The method used to obtain the general form of the coefficients of the characteristic polynomial is by adding up the determinant values of all directed induced subgraphs, cyclic or acyclic, of the directed cyclic friendship graph. Furthermore, the methods used to find theeigenvalues of the anti-Adjacency matrix of directed cyclic friendship graph are the substitution method and factorization method. The result of this researcharethe general form of the coefficients of the characteristic polynomial and the general form of the eigenvalues of the anti-Adjacency matrix depend on the number of triangles in directed cyclic friendship graph.

UR - http://www.scopus.com/inward/record.url?scp=85088299178&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1538/1/012007

DO - 10.1088/1742-6596/1538/1/012007

M3 - Conference article

AN - SCOPUS:85088299178

SN - 1742-6588

VL - 1538

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012007

T2 - 3rd International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2019

Y2 - 26 October 2019 through 27 October 2019

ER -