  We introduce an invariant of alternating knots and links (called here WRP),
namely a pair of integer polynomials associated with their two checkerboard
planar graphs from their minimal diagram. We prove that the invariant is
well-defined and give its values obtained from calculations for some knots in
the tables. This invariant is strong enough to distinguish all knots in the
tables with up to 10 crossings (including their mirror images). We compare the
strength of the new invariant with classical invariants, including the
three-variable Kauffman bracket.
