Choice Number and Energy of Graphs
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The energy of a graph G, denoted by E(G), is defined as the sum of the absolute values of all eigenvalues of G. It is proved that E(G)>= 2(n-χ(\bar{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 \bar{G}, χ(G), and ch(G) are the complement, the chromatic number, and the choice number of G, respectively.
to appear in Linear Algebra and its Applications
to appear in Linear Algebra and its Applications