Abstract
Given a graph G, its energy E ( G) is defined as the sum of the absolute values of the eigenvalues of G. The concept of the energy of a graph was introduced in the subject of chemistry by I. Gutman, due to its relevance to the total π-electron energy of certain molecules. In this paper, we show that if G is a graph on n vertices, then E(G) ≤ n 2 1 + n must hold, and we give an infinite family of graphs for which this bound is sharp.
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