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A graph is said to be determined by its adjacency spectrum (or to be a $DS$ graph, for short) if there is no other non-isomorphic graph with the same adjacency spectrum. Although all connected graphs of index less than 2 are known to be determined by their adjacency spectra, the classification of $DS$ graphs of index less than 2 is not complete yet. The purpose of this paper is to characterize all $DS$ graphs of index less than 2 with no $Z_{N}$ as a component.
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