Chemical applications of the Laplacian spectrum. VI. On the largest Laplacian eigenvalue of alkanes

Abstract

The largest Lapacian eigenvalue μ1 of the molecular graph is a quantity important in the theory of the photoelectron spectra of saturated hydrocarbons. It is shown that in the case of alkanes, the presence or absence of quaternary carbon atoms is the main structural feature on which μ1 depends. Within sets of all alkanes with a given number of carbon atoms the species (with and without quaternary carbons atoms) whose μ1-values are minimal and maximal are determined.