Extremal graphs and bounds for general Gutman index

Swathi Shetty; B. R. Rakshith; N. V. Sayinath Udupa; Swathi Shetty; B. R. Rakshith; N. V. Sayinath Udupa

doi:10.3934/math.20241470

AIMS Mathematics

2024, Volume 9, Issue 11: 30454-30471. doi: 10.3934/math.20241470

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Research article

Extremal graphs and bounds for general Gutman index

Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576 104, India

Received: 12 June 2024 Revised: 25 September 2024 Accepted: 27 September 2024 Published: 25 October 2024
MSC : 05C09, 05C12, 05C35

In this paper, we solved some open problems on general Gutman index. More precisely, we characterized unicyclic graphs with extremal general Gutman index for some $ a $ and $ b $. We presented a sharp bound on general Gutman index of $ G $ in terms of order and vertex connectivity of $ G $. Also, we obtained some bounds on general Gutman index in terms of order, general Randić index, diameter, and independence number of graph $ G $. In addition, QSPR analysis on various anticancer drug structures was carried out to relate their physicochemical properties with the general Gutman index of the structure for some $ a $ and $ b $.
- general Gutman index,
- general Randić index,
- vertex connectivity,
- QSPR modeling
Citation: Swathi Shetty, B. R. Rakshith, N. V. Sayinath Udupa. Extremal graphs and bounds for general Gutman index[J]. AIMS Mathematics, 2024, 9(11): 30454-30471. doi: 10.3934/math.20241470

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Abstract

In this paper, we solved some open problems on general Gutman index. More precisely, we characterized unicyclic graphs with extremal general Gutman index for some $ a $ and $ b $. We presented a sharp bound on general Gutman index of $ G $ in terms of order and vertex connectivity of $ G $. Also, we obtained some bounds on general Gutman index in terms of order, general Randić index, diameter, and independence number of graph $ G $. In addition, QSPR analysis on various anticancer drug structures was carried out to relate their physicochemical properties with the general Gutman index of the structure for some $ a $ and $ b $.

References

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