ON HERMITIAN ADJACENCY MATRICES

Hermitian matrices of directed graphs were introduced by Mohar and Guo. In this paper, we obtain bounds for the eigenvalues of these matrices. We first introduce the incidence matrix and then the Laplacian of these graphs, and then we obtain a condition for the cospectrality of these matrices with the underlying Laplacian matrix of these graphs. We prove that the Hermitian adjacency matrices of tournaments are almost non-singular and their smallest eigenvalue is not bounded from below as the number of vertices tends to infinity. We also provide a bound for a certain number of subgraphs in a tournament.

کلیدواژه ها:

Lee Weight ، Linear Code ، Generalized Lee Weight ، MLDR Code