A Survey of Some Open Questions in Reconstruction Numbers

Abstract

Frank Harary contributed numerous questions to a variety of topics in graph theory. One of his favourite topics was the Reconstruction Problem, which, in its first issue in \(1977\), the Journal of Graph Theory described as the major unsolved problem in the field. Together with Plantholt, Frank Harary initiated the study of reconstruction numbers of graphs. We shall here present a survey of some of the work done on reconstruction numbers, focusing mainly on the questions which this work leaves open.