Abstract
A graph containing no path of length three as an induced subgraph is called a cograph. In this article, we give a recursive definition of cographs in terms of the vertex duplication and co-duplication operations. We then establish that no cographs have eigenvalues in the interval (−1,0), generalizing the same known result for threshold graphs. As a consequence, we present combinatorial descriptions for the multiplicities of 0 and −1 as eigenvalues of cographs. This provides a short proof of a known result.
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