On the coefficients of the Laplacian characteristic polynomial of trees. (English) Zbl 1080.05519

Gutman, I.; Pavlović, Ljiljana

Bull., Cl. Sci. Math. Nat., Sci. Math. 127, No. 28, 31-40 (2003).

If \(\psi(T,\lambda)\) is the Laplacian characteristic polynomial of an \(n\)-vertex tree \(T\) and the \(c_i\) are its coefficients, then \(c_0=0\) and \(c_1=n\). Properties of \(c_2\) and \(c_3\) for special classes of trees are given.

Reviewer: Vojislav Petrović (Novi Sad)

MSC:

05C50	Graphs and linear algebra (matrices, eigenvalues, etc.)
05C12	Distance in graphs
05C05	Trees

Keywords:

Laplacian spectrum; distance in graphs; Wiener number