This analysis reveals limits on the wiener index related to the first zagreb index and coindex, highlighting characteristics of extremal graphs.
In this paper, we establish extremal results and bounds of Wiener index with respect to the sum of the first Zagreb index and the first Zagreb coindex of a graph given its minimum and maximum degrees together with its diameter. We have shown that nontrivial complete graphs correspond to extremal graphs.
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Mohammad et al. (2025) studied this question.
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