On a relation between the atom-bond connectivity and the first geometric-arithmetic indices

The atom-bond connectivity index ( A B C ) and the first geometric-arithmetic index ( G A ) are two well-known molecular descriptors, which are found to be useful tools in QSPR/QSAR investigations. In this work, we obtain a relation between these two indices for simple connected graphs on n ? 3 vertices with minimum degree at least s and maximum degree at most t , where 1 ? s ? t ? n - 1 and t ? 2 . Using this relation, we prove that if t ? 4 s 2 - 3 s + 1 , then the A B C index is always less than the G A index and this bound is best possible for s ? 2 .

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