Lower bounds for the energy of graphs - Akbar Jahanbani (AKCE International Journal of Graphs and Combinatorics, 2018)
Let G be a finite simple undirected graph with n vertices and m edges. The energy of a graph G , denoted by E ( G ) , is defined as the sum of the absolute values of the eigenvalues of G . In this paper we present lower bounds for E ( G ) in terms of number of vertices, edges, Randić index, minimum degree, diameter, walk and determinant of the adjacency matrix. Also we show our lower bound in (11) under certain conditions is better than the classical bounds given in Caporossi et al. (1999), Das (2013) and McClelland (1971). Keywords: Energy (of non-singular graph), Determinant of adjacency matrix, Randić index, Spectral radius