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On transmission irregular starlike trees

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  • Al-Yakoob, Salem
  • Stevanović, Dragan

Abstract

We characterize transmission irregular starlike trees with three branches, completing the work started by Alizadeh and Klavžar in [Appl. Math. Comput. 328 (2018), 113–118], where one particular case of such trees was characterized. We also answer one of the questions raised by Alizadeh and Klavžar by providing an infinite family of transmission irregular starlike trees of even order.

Suggested Citation

  • Al-Yakoob, Salem & Stevanović, Dragan, 2020. "On transmission irregular starlike trees," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    • Handle: RePEc:eee:apmaco:v:380:y:2020:i:c:s0096300320302265
    DOI: 10.1016/j.amc.2020.125257
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    References listed on IDEAS

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    1. Goubko, Mikhail, 2018. "Maximizing Wiener index for trees with given vertex weight and degree sequences," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 102-114.
    2. Klavžar, Sandi & Azubha Jemilet, D. & Rajasingh, Indra & Manuel, Paul & Parthiban, N., 2018. "General Transmission Lemma and Wiener complexity of triangular grids," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 115-122.
    3. Dobrynin, Andrey A., 2019. "Infinite family of 2-connected transmission irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 1-4.
    4. Alizadeh, Yaser & Klavžar, Sandi, 2018. "On graphs whose Wiener complexity equals their order and on Wiener index of asymmetric graphs," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 113-118.
    5. Sun, Qiang & Ikica, Barbara & Škrekovski, Riste & Vukašinović, Vida, 2019. "Graphs with a given diameter that maximise the Wiener index," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 438-448.
    6. Knor, Martin & Majstorović, Snježana & Škrekovski, Riste, 2018. "Graphs preserving Wiener index upon vertex removal," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 25-32.
    7. Zhang, Jie & Wang, Hua & Zhang, Xiao-Dong, 2019. "The Steiner Wiener index of trees with a given segment sequence," Applied Mathematics and Computation, Elsevier, vol. 344, pages 20-29.
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    Cited by:

    1. Anatoly Yu. Bezhaev & Andrey A. Dobrynin, 2022. "On Transmission Irregular Cubic Graphs of an Arbitrary Order," Mathematics, MDPI, vol. 10(15), pages 1-15, August.
    2. Sharon, Jane Olive & Rajalaxmi, T.M. & Klavžar, Sandi & Rajan, R. Sundara & Rajasingh, Indra, 2021. "Transmission in H-naphtalenic nanosheet," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    3. Bezhaev, Anatoly Yu. & Dobrynin, Andrey A., 2021. "On quartic transmission irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 399(C).

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