Ela Notes on Graphs with Least Eigenvalue
نویسندگان
چکیده
A new proof concerning the determinant of the adjacency matrix of the line graph of a tree is presented and an invariant for line graphs, introduced by Cvetković and Lepović, with least eigenvalue at least −2 is revisited and given a new equivalent definition [D. Cvetković and M. Lepović. Cospectral graphs with least eigenvalue at least −2. Publ. Inst. Math., Nouv. Sér., 78(92):51–63, 2005.]. Employing this invariant and other techniques, it is shown that the line graphs of double stars are determined by their adjacency spectra.
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