Abstract: We consider a weighted zeta function and a weighted L-function of a digraph D, and give determinant expressions of them. Furthermore, we show that a
weighted zeta function and a weighted L-function
of D are equal to that of the line digraph of
D,
respectively. As corollaries, we show that a zeta function and an L-function of D are equal
to thatof the line graph of D, respectively. Moreover, we
express characteristic polynomials of a weighted matrix and the adjacency matrix
of by
those of D
Keywords and phrases: characteristic polynomial, zeta
function, line digraph, L-function,
covering digraph.
