KNOTTED SYMMETRICAL GRAPHS

For a knotted graph in S-3 we define the vertex constant group, a quot ient of the fundamental group of the complement. For planar graphs the group is cyclic. For graphs with periodic symmetry the group is relat ed to the fundamental group of the branched cover of S-3 branched over knots contained in the quotient of the graph under the symmetry. Thes e tools are used to demonstrate that a large family of knotted graphs are not planar.