Spectrum, Kite graph, Lagrange series, zeros
A Lagrange series around adjustable expansion points to compute the eigenvalues of graphs, whose characteristic polynomial is analytically known, is presented. The computations for the kite graph P_nK_m, whose largest eigenvalue was studied by Stevanovic and Hansen [D. Stevanovic and P. Hansen. The minimum spectral radius of graphs with a given clique number. Electronic Journal of Linear Algebra, 17:110–117, 2008.], are illustrated. It is found that the first term in the Lagrange series already leads to a better approximation than previously published bounds.
Van Mieghem, Piet.
"A Lagrange series approach to the spectrum of the Kite",
Electronic Journal of Linear Algebra,
Volume 30, pp. 934-943.