Malaysian Journal of Mathematical Sciences, June 2025, Vol. 19, No. 2
On Eigenvalues of Complement Digraphs
Prayitno, M. I. A., Susanti, Y., Wahyuni, S., and Suparwanto, A.
Corresponding Email: swahyuni@ugm.ac.id
Received date: 13 July 2024
Accepted date: 2 March 2025
Abstract:
A digraph's antiadjacency matrix is defined as its complement's adjacency matrix. Therefore, we can distinguish the complement of digraphs by analysing the properties of their antiadjacency matrices. In this paper, our interest lies in exploring the properties of eigenvalues of the antiadjacency matrix of digraphs and establishing their relation to the characterisation of digraphs. Recent results regarding the eigenvalues of the antiadjacency matrices of certain classes of cyclic digraphs allow us to generalise the bounds of the spectral radius of a complement digraph. Additionally, we establish a connection between the bounds of the spectral radius of a complement digraph and the characterisation of the complement digraph. Since a digraph can be either cyclic or acyclic, we distinguish between the spectral radius of a cyclic and acyclic digraphs.
Keywords: acyclic digraph; adjacency matrix; antiadjacency matrix; complement digraphs; cyclic digraph; eigenvalues; spectral radius
