Characteristic polynomial and eigenvalues of the anti-adjacency matrix of cyclic directed prism graph

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Abstract

A prism graph is a graph which corresponds to the skeleton of an n-prism and therefore it is a cyclic simple graph. It is denoted Yn (n ≥ 3) where n is half the number of vertices. An n-prism graph has 2n vertices and 3n edges. In this paper, only regularly-directed cyclic prism graphs are investigated. The anti-adjacency matrix is applied as the graph representation. An anti-adjacency matrix of graph representation is a 0-1 matrix of size m × m where m is the number of vertices. The entry bij of an anti-adjacency matrix B(G) of directed graph G is 0 if there exists a directed edge from vertex vi to vertex vj and is 1 otherwise. The characteristic polynomial of the anti-adjacency matrix B(Yn) of directed cyclic prism graph Yn are obtained. The characteristic polynomial will be proved by observing the both cyclic and acyclic induced subgraphs of the directed cyclic prims graph. Furthermore, the anti-adjacency matrix of directed cyclic prism graph is found to have both real eigenvalues and complex eigenvalues which appear in conjugate pairs.

Original languageEnglish
Title of host publicationProceedings of the 4th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2018
EditorsTerry Mart, Djoko Triyono, Ivandini T. Anggraningrum
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735419155
DOIs
Publication statusPublished - 4 Nov 2019
Event4th International Symposium on Current Progress in Mathematics and Sciences 2018, ISCPMS 2018 - Depok, Indonesia
Duration: 30 Oct 201831 Oct 2018

Publication series

NameAIP Conference Proceedings
Volume2168
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference4th International Symposium on Current Progress in Mathematics and Sciences 2018, ISCPMS 2018
CountryIndonesia
CityDepok
Period30/10/1831/10/18

Keywords

  • Anti-adjacency matrix
  • characteristic polynomial
  • directed graph
  • eigenvalues
  • prism graph

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    Stin, R., Aminah, S., & Utama, S. (2019). Characteristic polynomial and eigenvalues of the anti-adjacency matrix of cyclic directed prism graph. In T. Mart, D. Triyono, & I. T. Anggraningrum (Eds.), Proceedings of the 4th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2018 [020052] (AIP Conference Proceedings; Vol. 2168). American Institute of Physics Inc.. https://doi.org/10.1063/1.5132479