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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish
Title of host publicationProceedings of the 5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019
EditorsTerry Mart, Djoko Triyono, Tribidasari Anggraningrum Ivandini
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735420014
DOIs
Publication statusPublished - 1 Jun 2020
Event5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019 - Depok, Indonesia
Duration: 9 Jul 201910 Jul 2019

Publication series

NameAIP Conference Proceedings
Volume2242
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019
CountryIndonesia
CityDepok
Period9/07/1910/07/19

Keywords

  • Adjacency matrix
  • cyclic directed graph
  • indegree Laplacian matrix
  • outdegree Laplacian matrix
  • prism graph

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    Stin, R., Aminah, S., Utama, S., & Silaban, D. R. (2020). Characteristic polynomials and eigenvalues of the adjacency matrix and the Laplacian matrix of cyclic directed prism graph. In T. Mart, D. Triyono, & T. A. Ivandini (Eds.), Proceedings of the 5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019 [030028] (AIP Conference Proceedings; Vol. 2242). American Institute of Physics Inc.. https://doi.org/10.1063/5.0008300