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Title:
A note on extremality of the first degree-based entropy
Authors:
Yuhong Yang
doi:
Volume
87
Issue
1
Year
2022
Pages
125-131
Abstract Let \(G\) be a connected graph of order \(n\) with degree sequence \(D(G) = [d_1, d_2, \ldots, d_n]\). The first degree-based entropy of \(G\) is defined as \[ I_1(G) = \ln\left(\sum_{i=1}^n d_i\right) - \frac{1}{\sum_{i=1}^n d_i} \sum_{i=1}^n (d_i\ln d_i) \] In this paper, we characterize the corresponding extremal graphs which attain the maximum value of \(I_1(G)\) among all \(k\)-cyclic graphs of order \(n\), where \(k \geq 1\).

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