Abstract
The energy \(E(G)\) of a graph \(G\), a quantity closely related to total \(\pi \)-electron energy, is equal to the sum of absolute values of the eigenvalues of \(G\). Two graphs \(G_a\) and \(G_b\) are said to be equienergetic if \(E(G_a)=E(G_b)\). In 2009 it was discovered that there are pairs of graphs for which the difference \(E(G_a)-E(G_b)\) is non-zero, but very small. Such pairs of graphs were referred to as almost equienergetic, but a precise criterion for almost–equienergeticity was not given. We now fill this gap.
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