Generalizing the McClelland Bounds for Total p-Electron Energy

In 1971 McClelland obtained lower and upper bounds for the total π-electron energy. We now formulate the generalized version of these bounds, applicable to the energy-like expression EX = ∑ i=1n |xi - x̄|, where x1, X2,..., xn are any real numbers, and x̄ is their arithmetic mean. In particular, if x1, X2,...,x n are the eigenvalues of the adjacency, Laplacian, or distance matrix of some graph G, then EX is the graph energy, Laplacian energy, or distance energy, respectively, of G. © 2008 Verlag der Zeitschrift für Naturforschung, Tübingen.