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Sets of cospectral graphs with least eigenvalue at least -2 and some related results

Cvetković Dragoš M. (University of Belgrade, Faculty of Electrical Engineering, Belgrade)
Lepović Mirko V. (University of Kragujevac, Faculty of Sciences, Kragujevac)

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 Co spectral 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