Camara and Haemers (2014) investigated when a complete graph with some edges deleted is determined by its adjacency spectrum (DAS for short). They claimed: for any m ? 6 and every large enough n one can obtain graphs which are not DAS by removing m edges from a complete graph K n . Let G n denote the set of all graphs obtained from a complete graph K n by deleting six edges. In this paper, we show that all graphs in G n are uniquely determined by their permanental spectra. However, we show that for each n ? 7 or n = 5 there is just one pair of nonisomorphic cospectral graphs in G n , and for n = 4 or 6 all graphs in G n are DAS.
['Tingzeng Wu', 'Heping Zhang']
Per-spectral and adjacency spectral characterizations of a complete graph removing six edges