ABSTRACT
This chapter discusses the biquandle and discusses a biquandle associated with a virtual link diagram and prove that this biquandle is invariant under the diagrammatic moves. The original application of the biquandle to virtual links occurs in the paper "Bi-oriented Quantum Algebras, and a Generalized Alexander Polynomial for Virtual Links" by L. Kauffman and D. Radford. The chapter considers a cycle with inserted edges. The thickened edges represent inserted edges while the thin edges are oriented edges from the original knot diagram. The outward pointing edges are each part of a cycle. But a cycle containing these edges must cross the cycle containing the inserted edges with a virtual crossing. The chapter describes the biquandle of the oriented virtual trefoil diagram using the labeling. The biquandle of a knot diagram is invariant under the diagrammatic moves.
