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.
|Journal||Journal of Physics: Conference Series|
|Publication status||Published - 23 Mar 2021|
|Event||4th International Conference on Combinatorics, Graph Theory, and Network Topology, ICCGANT 2020 - Jember, East Java, Indonesia|
Duration: 22 Aug 2020 → 23 Aug 2020