The ABS (atom-bond sum-connectivity) index of a graph G is denoted by ABS(G) and is defined as ∑xy∈E(G)(dx+dy)−1(dx+dy−2), where dx represents the degree of the vertex x in G. In this paper, we derive the best possible upper bounds on the ABS index for fixed-order trees possessing a given maximum degree, which provides a solution to the open problem proposed quite recently by Hussain, Liu and Hua.
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Maitreyi et al. (2024) studied this question.
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