Decomposition formulas of zeta functions of graphs and digraphs

AbstractWe give a decomposition formula of the zeta function of a regular covering of a graph G with respect to equivalence classes of prime, reduced cycles of G. Furthermore, we give a decomposition formula of the zeta function of a g-cyclic Γ-cover of a symmetric digraph D with respect to equivalence classes of prime cycles of D, for any finite group Γ and g∈Γ

On Preserving Structured Matrices Using Double Bracket Operators: Tridiagonal and Toeplitz Matrices

In the algebra of square matrices over the complex numbers, denotes Two problems are solved: (1) Find all Hermitian matrices M which have the following property: For every Hermitian matrix A, if A is tridiagonal, then so is (2) Find all Hermitian matrices M which have the following property: For every Hermitian matrix A, if A is Toeplitz, then so i