The characteristic polynomial of the Laplacian of graphs in [formula omitted]-linear classes

Abstract

In this work we deal with the characteristic polynomial of the Laplacian of a graph. We present some general results about the coefficients of this polynomial. We present families of graphs, for which the number of edges m is given by a linear function of the number of vertices n. In some of these graphs we can find certain coefficients of the above-named polynomial as functions just of n.