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The paper gives a short survey of the most important lower and upper bounds for the total π-electron energy, i.e., the graph energy (E). In addition, a new lower and a new upper bound for E are deduced, valid for general molecular graphs. The strengthened versions of these estimates, valid for alternant conjugated hydrocarbons, are also reported [ABSTRACT FROM AUTHOR]

The atom-bond connectivity index (ABC) is a degree-based molecular structure descriptor with well-documented chemical applications. In 2010, a distance-based new variant of this index (ABCGG) was proposed. Hitherto, the relation between ABC and ABCGG has not been analyzed. In this paper, the basic characteristics of this relation are established. In particular, ABC and ABCGG are not correlated and both cases ABC > ABCGG and ABC < ABCGG may occur in the case of (structurally similar) molecules. However, in the case of benzenoid hydrocarbons, ABC always exceeds ABCGG. [ABSTRACT FROM AUTHOR]