Polynomial reconstruction for certain subclasses of disconnected graphs

Abstract

The Reconstruction Conjecture (RC) and the Polynomial Reconstruction Problem (PRP) are two of the open problems in algebraic graph theory. They have been resolved successfully for a number of different classes and subclasses of graphs. This paper gives proofs for a positive conclusion for the polynomial reconstruction of the following three subclasses of the class of disconnected graphs. These subclasses are disconnected graphs with two unicyclic components, the bidegreed disconnected graphs with regular components and the disconnected graphs with a wheel as one component.