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Stepwise transmission irregular graphs

Author

Listed:
  • Dobrynin, Andrey A.
  • Sharafdini, Reza

Abstract

The distance d(u, v) between vertices u and v of a connected graph G is defined as the number of edges in a shortest path connecting them. The transmission of a vertex v of G is the sum of distances from v to all the other vertices of G. A graph is stepwise transmission irregular (STI) if the transmissions of any two of its adjacent vertices differ by exactly one. Some basic properties of STI graphs are established and infinite families are constructed.

Suggested Citation

  • Dobrynin, Andrey A. & Sharafdini, Reza, 2020. "Stepwise transmission irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    • Handle: RePEc:eee:apmaco:v:371:y:2020:i:c:s0096300319309415
    DOI: 10.1016/j.amc.2019.124949
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    References listed on IDEAS

    as
    1. Gutman, Ivan, 2018. "Stepwise irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 234-238.
    2. Dobrynin, Andrey A., 2019. "Infinite family of 2-connected transmission irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 1-4.
    3. 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.
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    Citations

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    Cited by:

    1. Lin, Hongying & Zhou, Bo, 2021. "Which numbers are status differences?," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    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).
    4. Al-Yakoob, Salem & Stevanović, Dragan, 2022. "On stepwise transmission irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 413(C).

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