Ihara's Formula
Ihara showed that for regular graphs the zeta function is a rational function. If G is k-regular with adjacency matrix A then
where χ is the circuit rank.
The Ihara zeta-function is in fact always the reciprocal of a polynomial:
where T is Hashimoto's edge adjacency operator. Hyman Bass gave a determinant formula involving the adjacency operator.
Read more about this topic: Ihara Zeta Function
Famous quotes containing the word formula:
“For the myth is the foundation of life; it is the timeless schema, the pious formula into which life flows when it reproduces its traits out of the unconscious.”
—Thomas Mann (1875–1955)