Weakly Cospectral Graphs
Matematičeskie zametki, Tome 75 (2004) no. 4, pp. 614-623

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It is proved that any set of finite pairwise nonisomorphic weakly cospectral connected pseudographs, as well as any set of pseudodigraphs satisfying various additional conditions, is finite.
@article{MZM_2004_75_4_a10,
     author = {S. P. Strunkov},
     title = {Weakly {Cospectral} {Graphs}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {614--623},
     publisher = {mathdoc},
     volume = {75},
     number = {4},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_4_a10/}
}
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S. P. Strunkov. Weakly Cospectral Graphs. Matematičeskie zametki, Tome 75 (2004) no. 4, pp. 614-623. http://geodesic.mathdoc.fr/item/MZM_2004_75_4_a10/