Abstract
Harary's edge reconstruction conjecture states that a graph G=( V, E) with at least four edges is uniquely determined by the multiset of its edge-deleted subgraphs, i.e. the graphs of the form G− e for e∈ E. It is well-known that this multiset uniquely determines the degree sequence of a graph with at least four edges. In this note we generalize this result by showing that the degree sequence of a graph with at least four edges is uniquely determined by the set of the degree sequences of its edge-deleted subgraphs with one well-described class of exceptions. Moreover, the multiset of the degree sequences of the edge-deleted subgraphs always allows one to reconstruct the degree sequence of the graph.
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