TY - GEN

T1 - Characteristic polynomials and eigenvalues of the adjacency matrix and the Laplacian matrix of cyclic directed prism graph

AU - Stin, R.

AU - Aminah, S.

AU - Utama, S.

AU - Silaban, D. R.

N1 - Publisher Copyright:
© 2020 Author(s).

PY - 2020/6/1

Y1 - 2020/6/1

N2 - An adjacency matrix A(G) of directed graph G is an m×m matrix consisting of only entries 0 and 1, where m is the number of vertices of G. The entry aij is equal to 1 if there exists a directed edge from vertex vi to vertex vj, otherwise it is equal to 0. Let D(G) be a diagonal matrix of size m×m with each of its main diagonal entry being the degree of the corresponding vertex of directed graph G. Then the matrix L(G) = D(G) - A(G) is called the Laplacian matrix of G. Since a directed graph has two types of degrees namely indegree and outdegree, they result in directed graphs also having the both types of its Laplacian matrices. In this study, the adjacency matrix and the Laplacian matrix of cyclic directed prism graph are investigated. The general form of the coefficients of polynomial characteristic of the Adjacency matrix and Laplacian matrix, respectively is obtained by applying the row reduction method in linear algebra, whereas the general form of the eigenvalues of the polynomial characteristic of the Adjacency matrix and Laplacian matrix, respectively is obtained by factorization and substitution methods.

AB - An adjacency matrix A(G) of directed graph G is an m×m matrix consisting of only entries 0 and 1, where m is the number of vertices of G. The entry aij is equal to 1 if there exists a directed edge from vertex vi to vertex vj, otherwise it is equal to 0. Let D(G) be a diagonal matrix of size m×m with each of its main diagonal entry being the degree of the corresponding vertex of directed graph G. Then the matrix L(G) = D(G) - A(G) is called the Laplacian matrix of G. Since a directed graph has two types of degrees namely indegree and outdegree, they result in directed graphs also having the both types of its Laplacian matrices. In this study, the adjacency matrix and the Laplacian matrix of cyclic directed prism graph are investigated. The general form of the coefficients of polynomial characteristic of the Adjacency matrix and Laplacian matrix, respectively is obtained by applying the row reduction method in linear algebra, whereas the general form of the eigenvalues of the polynomial characteristic of the Adjacency matrix and Laplacian matrix, respectively is obtained by factorization and substitution methods.

KW - Adjacency matrix

KW - cyclic directed graph

KW - indegree Laplacian matrix

KW - outdegree Laplacian matrix

KW - prism graph

UR - http://www.scopus.com/inward/record.url?scp=85086673414&partnerID=8YFLogxK

U2 - 10.1063/5.0008300

DO - 10.1063/5.0008300

M3 - Conference contribution

AN - SCOPUS:85086673414

T3 - AIP Conference Proceedings

BT - Proceedings of the 5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019

A2 - Mart, Terry

A2 - Triyono, Djoko

A2 - Ivandini, Tribidasari Anggraningrum

PB - American Institute of Physics Inc.

T2 - 5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019

Y2 - 9 July 2019 through 10 July 2019

ER -