Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 3

Inequalities on the geometric-arithmetic index

Sayfa
778–794
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The objective of the work we present here is twofold: First, obtaining new relations connecting the geometric-arithmetic index with other topological indices; second, to characterize graphs which are extremal with respect to those relations.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Although the notion of geometric-arithmetic index has been introduced in the chemical graph theory these past years, it has already proved to be useful.
📊
Temel Bulgular & Veri:Although the notion of geometric-arithmetic index has been introduced in the chemical graph theory these past years, it has already proved to be useful.
💡
Sonuç & Katkı:The objective of the work we present here is twofold: First, obtaining new relations connecting the geometric-arithmetic index with other topological indices; second, to characterize graphs which are extremal with respect to those relations.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:geometric-arithmetic index · vertex-degree-based topological index · variable Zagreb index

Abstract

Although the notion of geometric-arithmetic index has been introduced in the chemical graph theory these past years, it has already proved to be useful. The objective of the work we present here is twofold: First, obtaining new relations connecting the geometric-arithmetic index with other topological indices; second, to characterize graphs which are extremal with respect to those relations.

🔖

Bu Makaleye Atıf Yap

GRANADOS, A., PORTILLA, A., RODRIGUEZ, J. M., SIGARRETA, J. M. (2022). Inequalities on the geometric-arithmetic index. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 778–794. https://ajindex.com/articles/529534

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (20)

  1. H. Abdo, D. Dimitrov and I. Gutman, On extremal trees with respect to the F-index, Kuwait J. Sci. 44 (3) 1–8, 2017
  2. M.O. Albertson, The irregularity of a graph, Ars Comb. 46, 219–225, 1997
  3. A. Ali, I. Gutman, E. Milovanović and I. Milovanović, Sum of Powers of the Degrees of Graphs: Extremal Results and Bounds, MATCH Commun. Math. Comput. Chem. 80, 5–84, 2018
  4. V. Andova and M. Petrusevski, Variable Zagreb Indices and Karamataís Inequality, MATCH Commun. Math. Comput. Chem. 65, 685–690, 2011
  5. M. Aouchiche and P. Hansen, Comparing the geometric-arithmetic Index and the spectral radius of graphs, MATCH Commun. Math. Comput. Chem. 84 (2), 473–482, 2020
  6. M. Aouchiche and V. Ganesan, Adjusting geometric-arithmetic index to estimate boil- ing point, MATCH Commun. Math. Comput. Chem. 84, 483–497, 2020
  7. M. Aouchiche, I. El Hallaoui and P. Hansen, Geometric-Arithmetic index and mini- mum degree of connected graphs, MATCH Commun. Math. Comput. Chem. 83 (1), 179–188, 2020
  8. Z. Che and Z. Chen, Lower and Upper Bounds of the Forgotten Topological Index, MATCH Commun. Math. Comput. Chem. 76, 635–648, 2016
  9. Y. Chen and B. Wu On the geometric-arithmetic index of a graph, Discrete Appl. Math. 254, 268–273, 2019
  10. K.C. Das, On geometric-arithmetic index of graphs, MATCH Commun. Math. Com- put. Chem. 64, 619–630, 2010
  11. K.C. Das, I. Gutman and B. Furtula, On first geometric-arithmetic index of graphs, Discrete Appl. Math. 159, 2030–2037, 2011
  12. K.C. Das, I. Gutman and B. Furtula, Survey on Geometric-Arithmetic Indices of Graphs, MATCH Commun. Math. Comput. Chem. 65, 595–644, 2011
  13. S.S. Dragomir, A Survey On Cauchy-Bunyakovosky-Schwarz Type Discrete Inequali- ties, J. Inequal. Pure and Appl. Math. 4 (3), Art. 63, 2003
  14. M. Drmota, Random Trees: An Interplay Between Combinatorics and Probability, Springer, Wien-New York, 2009
  15. M. Eliasi, A. Iranmanesh and I. Gutman, Multiplicative versions of first Zagreb index, Commun. Math. Comput. Chem. 68 (1), 217–230, 2012
  16. G.H. Fath-Tabar, Old and New Zagreb Indices of Graphs, MATCH Commun. Math. Comput. Chem. 65, 79–84, 2011
  17. B. Furtula and I. Gutman, A forgotten topological index, J. Math. Chem. 53 (4), 1184–1190, 2015
  18. X. Guo and Y. Gao Arithmetic-geometric spectral radius and energy of graphs, MATCH Commun. Math. Comput. Chem. 83, 651–660, 2020
  19. I. Gutman, Degree–based topological indices, Croat. Chem. Acta 86, 351–361, 2013
  20. I. Gutman and K.C. Das,