Abstract
Some new constructions for families of cospectral graphs are derived, and some old ones are considerably generalized. One of our new constructions is sufficiently powerful to produce an estimated 72% of the 51039 graphs on 9 vertices which do not have unique spectrum. In fact, the number of graphs of ordern without unique spectrum is believed to be at leastαn 3 g −1 for someα>0, whereg n is the number of graphs of ordern andn ≥ 7.
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Godsil, C.D., McKay, B.D. Constructing cospectral graphs. Aeq. Math. 25, 257–268 (1982). https://doi.org/10.1007/BF02189621
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DOI: https://doi.org/10.1007/BF02189621