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Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 4

The Second and Third Geometric-Arithmetic Indices of Unicyclic Graphs

Ping LIU
Bolian LIU
Pages
555–562
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this paper, we obtain inequalities between the two indices for unicyclic graphs.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Gutman (A new geometricarithmetic index, J.
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Key Findings & Data:Chem. 47, 477–486, 2010) proposed the second geometric-arithmetic index GA2 and B.
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Conclusion & Impact:In this paper, we obtain inequalities between the two indices for unicyclic graphs.
🔬Design:Research Article
📍Scope:2010 Verileri
⚙️Variables:Distance between vertex and edge · Geometric-arithmetic index · Unicyclic graph

Abstract

Recently, G. Fath-Tabar, B. Furtula and I. Gutman (A new geometricarithmetic index, J. Math. Chem. 47, 477–486, 2010) proposed the second geometric-arithmetic index GA2 and B. Zhou, I. Gutman, B. Furtula and Z. Du (On two types of geometric-arithmetic index, Chem. Phys. Lett. 482, 153–155, 2009) put forward the third geometricarithmetic index GA3, respectively. In (Gutman, I. and Furtula, B. Estimating the second and third geometric-arithmetic indices, Hacet. J. Math. Stat. 40 (1), 69–76, 2011), inequalities between GA2 and GA3 for trees, with the number of vertices and the number of pendent vertices, were obtained by I. Gutman and B. Furtula. In this paper, we obtain inequalities between the two indices for unicyclic graphs.

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Cite This Article

LIU, P., LIU, B. (2022). The Second and Third Geometric-Arithmetic Indices of Unicyclic Graphs. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 4, 555–562. https://ajindex.com/articles/530584

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References (4)

  1. Fath-Tabar, G., Furtula, B. and Gutman, I. A new geometric-arithmetic index, J. Math. Chem. 47, 477–486, 2010.
  2. Furtula, B. and Gutman, I. Geometric-arithmetic indices, in: I. Gutman, B. Furtula (Eds.), Novel Molecular Structure-Descriptors - Theory and Applications I, Univ. Kragujevac, Kragu- jevac, 137–172, 2010.
  3. Gutman, I. and Furtula, B. Estimating the second and third geometric-arithmetic indices, Hacet. J. Math. Stat. 40 (1), 69–76, 2011. Vukiˇcevi´c, D. and Furtula, B. Topological index based on the ratios of geometrical and arith- metical means of end-vertex degrees of edges, J. Math. Chem. 46, 1369–1376, 2009.
  4. Zhou, B., Gutman, I., Furtula, B. and Du, Z. On two types of geometric-arithmetic index, Chem. Phys. Lett. 482, 153–155, 2009.