Geodesic
Sets of cospectral graphs with least eigenvalue at least -2 and some related results
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 29 (2004) no. 1 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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In this paper we study the phenomenon of cospectrality in generalized line graphs and in exceptional graphs. The paper contains a table of sets of cospectral graphs with least eigenvalue at least $-2$ and at most 8 vertices together with some comments and theoretical explanations of the phenomena suggested by the table. In particular, we prove that the multiplicity of the number $0$ in the spectrum of a generalized line graph $L(G)$ is at least the number of petals of the corresponding root graph $G$.
Keywords: graphs, eigenvalues, least eigenvalue, cospectral graphs 
@article{BASS_2004_29_1_a5,
     author = {D. Cvetkovi\'c and M. Lepovi\'c},
     title = {Sets of cospectral graphs with least eigenvalue at least -2 and some related results},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {85 - 102},
     year = {2004},
     volume = {29},
     number = {1},
     zbl = {1077.05059},
     url = {http://geodesic.mathdoc.fr/item/BASS_2004_29_1_a5/}
}
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D. Cvetković; M. Lepović. Sets of cospectral graphs with least eigenvalue at least -2 and some related results. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 29 (2004) no. 1. http://geodesic.mathdoc.fr/item/BASS_2004_29_1_a5/