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

DOI

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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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  - 10.2991/miseic-18.2018.3
ID  - Solihin2018/07
ER  -