Proceedings of the Mathematics, Informatics, Science, and Education International Conference (MISEIC 2018)

Properties of Anti-Adjacency Matrix of Cyclic Directed Windmill Graph K ⃗(4,n)

Authors
Muhammad Sabili Robbi Solihin, S Aminah, Suarsi Utama
Corresponding Author
Muhammad Sabili Robbi Solihin
Available Online July 2018.
DOI
https://doi.org/10.2991/miseic-18.2018.3How to use a DOI?
Keywords
Graph; Anti-adjacency matrix; Characteristic polynomial; Eigenvalue
Abstract

Anti-adjacency matrix is a way to represent a directed graph as a square matrix, whose entries show whether there is a directed edge from a vertex to another one. This paper focuses on the properties of anti-adjacency matrix of windmill graph (4,), such as its characteristic polynomial and eigenvalues. The general form of characteristic polynomial is established by analyzing the degree of vertices and edges, and the cyclic induced subgraphs. Furthermore, the eigenvalues of a windmill graph (4,) and its multiplicity are derived from the general form of its characteristic polynomial.

Copyright
© 2018, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Volume Title
Proceedings of the Mathematics, Informatics, Science, and Education International Conference (MISEIC 2018)
Series
Advances in Intelligent Systems Research
Publication Date
July 2018
ISBN
978-94-6252-601-3
ISSN
1951-6851
DOI
https://doi.org/10.2991/miseic-18.2018.3How to use a DOI?
Copyright
© 2018, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - CONF
AU  - Muhammad Sabili Robbi Solihin
AU  - S Aminah
AU  - Suarsi Utama
PY  - 2018/07
DA  - 2018/07
TI  - Properties of Anti-Adjacency Matrix of Cyclic Directed Windmill Graph K ⃗(4,n)
BT  - Proceedings of the Mathematics, Informatics, Science, and Education International Conference (MISEIC 2018)
PB  - Atlantis Press
SP  - 9
EP  - 12
SN  - 1951-6851
UR  - https://doi.org/10.2991/miseic-18.2018.3
DO  - https://doi.org/10.2991/miseic-18.2018.3
ID  - Solihin2018/07
ER  -