Graph spectra (Q1916101)

The \(k\)-spectrum of a graph \(G\) is the set of all nonnegative integers that occur as the size of an induced \(k\)-vertex subgraph of \(G\). The authors determine the minimum order and size of a graph whose \(k\)-spectrum contains all the numbers \(0,1, \dots, {k \choose 2}\). They also study the sets that are \(k\)-spectra of some graphs. Reviewer's remark. The title of the paper is a little bit misleading since under the spectrum of a graph a reader would usually understand the spectrum of a matrix associated to the graph in a certain way.