Research article

Unicyclic graphs with extremal exponential Randić index

  • Received: 08 June 2021 Accepted: 05 October 2021 Published: 13 October 2021
  • Recently the exponential Randić index $ {{\rm e}^{\chi}} $ was introduced. The exponential Randić index of a graph $ G $ is defined as the sum of the weights $ {{\rm e}^{{\frac {1}{\sqrt {d \left(u \right) d \left(v \right) }}}}} $ of all edges $ uv $ of $ G $, where $ d(u) $ denotes the degree of a vertex $ u $ in $ G $. In this paper, we give sharp lower and upper bounds on the exponential Randić index of unicyclic graphs.

    Citation: Qian Lin, Yan Zhu. Unicyclic graphs with extremal exponential Randić index[J]. Mathematical Modelling and Control, 2021, 1(3): 164-171. doi: 10.3934/mmc.2021015

    Related Papers:

  • Recently the exponential Randić index $ {{\rm e}^{\chi}} $ was introduced. The exponential Randić index of a graph $ G $ is defined as the sum of the weights $ {{\rm e}^{{\frac {1}{\sqrt {d \left(u \right) d \left(v \right) }}}}} $ of all edges $ uv $ of $ G $, where $ d(u) $ denotes the degree of a vertex $ u $ in $ G $. In this paper, we give sharp lower and upper bounds on the exponential Randić index of unicyclic graphs.



    加载中


    [1] B. Bollobás, P. Erdös, Graphs of extremal weights, Ars Combin., 50 (1998), 225–233.
    [2] Z. Du, B. Zhou, On Randić indices of trees, unicyclic graphs, and bicyclic graphs, Int. J. Quantum. Chem., 111 (2011), 2760–2770.
    [3] X. Li, Y. Yuan, Sharp bounds for the general Randić index, MATCH Commun. Math. Comput. Chem., 51 (2004), 155–166.
    [4] Y. Hu, X. Li, Y. Yuan, Trees with minimum general Randić index, MATCH Commun. Math. Comput. Chem., 52 (2004), 119–128.
    [5] Y. Hu, X. Li, Y. Yuan, Trees with maximum general Randić index, MATCH Commun. Math. Comput. Chem., 52 (2004), 129–146.
    [6] X. Li, Y. Shi, T. Xu, Unicyclic graphs with maximum general Randić index for $\alpha >0$, MATCH Commun. Math. Comput. Chem., 56 (2006), 557–570.
    [7] B. Wu, L. Zhang, Unicyclic graphs with minimum general Randić index, MATCH Commun. Math. Comput. Chem., 54 (2005), 455–464.
    [8] J. Gao, M. Lu, On the Randić index of unicyclic graphs, MATCH Commun. Math. Comput. Chem., 53 (2005), 377–384.
    [9] I. Gutman, B. Furtula, Recent results in the theory of Randić index, Univ. Kragujevac, 2008.
    [10] I. Gutman, B. Furtula, V. Katanić, Randić index and information, AKCE Int. J. Graphs Comb., 15 (2018), 307–312. doi: 10.1016/j.akcej.2017.09.006
    [11] G. Liu, Y. Zhu, J. Cai, On the Randić index of unicyclic graphs with girth $g$, MATCH Commun. Math. Comput. Chem., 58 (2007), 127–138.
    [12] J. Rada, S. Bermudo, Is every graph the extremal value of a vertex-degree-based topological index?, MATCH Commun. Math. Comput. Chem., 81 (2019), 315–323.
    [13] S. O. Y. Shi, Sharp bounds for the Randić index of graphs with given minimum and maximum degree, Discrete Appl. Math., 247 (2018), 111–115. doi: 10.1016/j.dam.2018.03.064
    [14] J. Rada, Exponential vertex-degree-based topological indices and discrimination, MATCH Commun. Math. Comput. Chem., 82 (2019), 29–41.
    [15] R. Cruz, M. Londoño, J. Rada, Minimal value of the exponential of the generalized Randić index over trees, MATCH Commun. Math. Comput. Chem., 85 (2021), 427–440.
    [16] R. Cruz, J. Monsalve, J. Rada, Trees with maximum exponential Randić index, Discrete Appl. Math., 283 (2020), 634–643. doi: 10.1016/j.dam.2020.03.009
    [17] D. Stevanović, A. Ilić. On the Laplacian coefficients of unicyclic graphs, Linear Algebra Appl., 430 (2009), 2290–2300. doi: 10.1016/j.laa.2008.12.006
  • Reader Comments
  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2215) PDF downloads(110) Cited by(0)

Article outline

Figures and Tables

Figures(6)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog