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 -