Choice number and energy of graphs

AbstractThe energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of the adjacency matrix of G. It is proved that E(G)⩾2(n-χ(G¯))⩾2(ch(G)-1) for every graph G of order n, and that E(G)⩾2ch(G) for all graphs G except for those in a few specified families, where G¯, χ(G), and ch(G) are the complement, the chromatic number, and the choice number of G, respectively