Improved McClelland and Koolen-Moulton bounds for the energy of graphs.

Given a graph G with n vertices and m edges, the term energy of graph E(G) was introduced by Gutman in chemistry, due to its relevance to the total π ― electron energy of carbon compounds. In 1971 McClelland obtained both lower and upper bounds for π 8213; electron energy. An improved upper bound was obtained by Koolen-Moulton in 2001. The lower and upper bounds for E(G) obtained in this paper are better than McClelland and Koolen-Moulton bounds. Also we obtained an upper bound for graph energy in terms of n as E(G) ≤ n/2[ 1 + √ n-2/2]. [ABSTRACT FROM AUTHOR]