Properties of adjacency, in-degree Laplacian, and out-degree Laplacian matrices of directed cyclic sun graph

Muhammad Irfan Arsyad Prayitno, Suarsih Utama, Siti Aminah, Denny Riama Silaban

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

Abstract

A directed graph can be represented by several matrix representations, such as adjacency matrix, in-degree Laplacian matrix, and out-degree Laplacian matrix. A directed cyclic sun graph is a directed graph which is obtained by adding a directed edge and a vertex called the outer vertex as its tail to every vertex in the directed cycle graph. The inner vertices always form a directed cycle graph. The directed edges in the cycle graph is oriented in such a away so that clockwise. In this paper we give the properties of adjacency, in-degree Laplacian, and out-degree Laplacian matrices of directed cyclic sun graph such as characteristic polynomial and eigenvalues. The eigenvalues of the matrices mentioned above can be real or complex numbers.

Original languageEnglish
Title of host publicationProceedings of the 8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019
Subtitle of host publicationDeepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations
EditorsHerni Utami, Fajar Adi Kusumo, Nanang Susyanto, Yeni Susanti
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735419438
DOIs
Publication statusPublished - 19 Dec 2019
Event8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations - Yogyakarta, Indonesia
Duration: 29 Jul 20191 Aug 2019

Publication series

NameAIP Conference Proceedings
Volume2192
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations
CountryIndonesia
CityYogyakarta
Period29/07/191/08/19

Keywords

  • adjacency matrix
  • characteristic polynomials
  • directed cyclic sun graph
  • eigenvalues
  • in-degree Laplacian matrix
  • out-degree Laplacian matrix

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  • Cite this

    Prayitno, M. I. A., Utama, S., Aminah, S., & Silaban, D. R. (2019). Properties of adjacency, in-degree Laplacian, and out-degree Laplacian matrices of directed cyclic sun graph. In H. Utami, F. A. Kusumo, N. Susyanto, & Y. Susanti (Eds.), Proceedings of the 8th SEAMS-UGM International Conference on Mathematics and Its Applications 2019: Deepening Mathematical Concepts for Wider Application through Multidisciplinary Research and Industries Collaborations [040011] (AIP Conference Proceedings; Vol. 2192). American Institute of Physics Inc.. https://doi.org/10.1063/1.5139137