Reconstructing Digraphs from Partial Dadecks

Abstract D − v together with the degree triple of v in D is called a degree associated card or dacard of digraph D. The collection of all dacards of Dis called the dadeck of D. Digraph reconstruction conjecture (DRC) was disproved when Stockmeyer exhibited infinite families of counterexamples. All the digraphs in these families are contained in classes of digraphs that are already proved to be reconstructible from their dadecks. Using the concept of reconstruction numbers, it is proved that they are also reconstructible from proper subdecks of their dadecks, strengthening the claim that ‘reconstruction from dacards’ is the correct extension of graph reconstruction to digraphs.