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G-2019-58

Geometric-arithmetic index and minimum degree of connected graphs

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In the present paper, we prove lower and upper bounds for each of the ratios GA/δ, as well as a lower bound on GA/δ, in terms of the order n, over the class of connected graphs on n vertices, where GA and δ denote the geometric-arithmetic index and the minimum degree, respectively. We also characterize the extremal graphs corresponding to each of those bounds. In order to prove our results, we provide a modified statement of a well-known lower bound on the geometric-arithmetic index in terms of minimum degree.

, 11 pages

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Geometric-arithmetic index and minimum degree of connected graphs
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MATCH, Communications in Mathematical and in Computer Chemistry, 83, 179–188, 2020 référence BibTeX