Characteristic polynomial and eigenvalues of anti-adjacency matrix of directed unicyclic corona graph

Abstract

A directed graph can be represented by several matrix representations, such as the anti-adjacency matrix. This paper discusses the general form of characteristic polynomial and eigenvaluesof the anti-adjacencymatrix of directed unicyclic corona graph. The characteristic polynomial of the anti-adjacency matrix can be found by counting the sum of the determinant of the anti-adjacency matrix of the directed cyclic inducedsubgraphs and the directed acyclic induced subgraphs from the graph. The eigenvalues of the anti-adjacency matrix can be real or complex numbers. We prove that the coefficient of the characteristic polynomial and the eigenvalues of the anti-adjacency matrix of directed unicyclic corona graph can be expressed in the function form that depends on the number of subgraphs contained in thedirected unicyclic corona graphs.