  A state model for Kauffman polynomial of Dubrovnik-version is given. Based on
the state model, the Gauss diagram formulae for Vassiliev invariants are given
from the coefficients of Kauffman polynomial following the method of Chmutov
and Polyak. Some arrow diagram identities are given to simplify the Gauss
diagram formulae of order 3, which give Polyak-Viro and Chmutov-Polyak formulae
for the Vassiliev invariant of order 3. The models of Kauffman polynomial and
HOMFLY-PT polynomial give different Gauss diagram expressions when specializing
to Jones poynomial.
