Characteristics polynomial of normalized Laplacian for trees

Abstract

Here, we find the characteristics polynomial of normalized Laplacian of a tree. The coefficients of this polynomial are expressed by the higher order general Randić indices for matching, whose values depend on the structure of the tree. We also find the expression of these indices for starlike tree and a double-starlike tree, $H_m(p,q)$. Moreover, we show that two cospectral $H_m(p,q)$ of the same diameter are isomorphic.

11 pages, 1 table, 2 Figures

References in corpus (3)

• Effect on normalized graph Laplacian spectrum by motif attachment and duplication
• Minimum vertex covers and the spectrum of the normalized Laplacian on trees
• On the spectrum of the normalized graph Laplacian