Graph spectra Original Research Article

The k-spectrum sk(G) of a graph G is the set of all positive integers that occur as the size of an induced k-vertex subgraph of G. In this paper we determine the minimum order and size of a graph G with sk (G) = {0, 1, …,(2k)} and consider the more general question of describing those sets S ⊆ {0,1, … ,(2k)} such that S = sk(G) for some graph G.