<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Graph theory has applications in various fields due to offering important tools such as topological indices. Among the topological indices, the Randić index is simple and of great importance. The Randić index of a graph 𝒢 can be expressed as <inline-formula>
<alternatives>
<inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_ausm-2022-0016_eq_001.png"></inline-graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>R</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mo>=</mo><msub><mo>∑</mo><mrow><mi>x</mi><mi>y</mi><mo>∈</mo><mi>Y</mi><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mrow></msub><mrow><mfrac><mn>1</mn><mrow><msqrt><mrow><mi>τ</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mi>τ</mi><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow></mrow></msqrt></mrow></mfrac></mrow></mrow></math>
<tex-math>R\left( G \right) = \sum\nolimits_{xy \in Y\left( G \right)} {{1 \over {\sqrt {\tau \left( x \right)\tau \left( y \right)} }}}</tex-math>
</alternatives>
</inline-formula>, where 𝒴(𝒢) represents the edge set and τ(<italic>x</italic>) is the degree of vertex <italic>x</italic>. In this paper, considering the importance of the Randić index and applications two-trees graphs, we determine the first two minimums among the two-trees graphs.</p>
</abstract>

Graph theory has applications in various fields due to offering important tools such as topological indices. Among the topological indices, the Randić index is simple and of great importance. The Randić index of a graph 𝒢 can be expressed as 


R(G)=∑xy∈Y(G)1τ(x)τ(y)
R\left( G \right) = \sum\nolimits_{xy \in Y\left( G \right)} {{1 \over {\sqrt {\tau \left( x \right)\tau \left( y \right)} }}}

, where 𝒴(𝒢) represents the edge set and τ(x) is the degree of vertex x. In this paper, considering the importance of the Randić index and applications two-trees graphs, we determine the first two minimums among the two-trees graphs.

Extremal trees for the Randić index

Department of Computer and Information Sciences

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Extremal trees for the Randić index"}

Graph theory has applications in various fields due to offering important tools such as topological indices. Among the topological indices, the Randić index is...

Extremal trees for the Randić index

Published Online: Jan 19, 2023

Page range: 239 - 249

Received: Oct 27, 2021

DOI: https://doi.org/10.2478/ausm-2022-0016

Keywords
Randić index, two-tree graphs

© 2022 Akbar Jahanbani et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Extremal trees for the Randić index

Published Online: Jan 19, 2023

Page range: 239 - 249

Received: Oct 27, 2021

DOI: https://doi.org/10.2478/ausm-2022-0016

KeywordsRandić index, two-tree graphs

© 2022 Akbar Jahanbani et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
Randić index, two-tree graphs