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Infinite family of 2-connected transmission irregular graphs

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  • Dobrynin, Andrey A.

Abstract

Distance between two vertices is the number of edges in the shortest path connecting them in a connected graph G. The transmission of a vertex v is the sum of distances from v to all the other vertices of G. If transmissions of all vertices are mutually distinct, then G is a transmission irregular graph. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees were presented in [4]. The following problem was posed in [4]: do there exist infinite families of 2-connected transmission irregular graphs? In this paper, an infinite family of such graphs is constructed.

Suggested Citation

  • Dobrynin, Andrey A., 2019. "Infinite family of 2-connected transmission irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 1-4.
    • Handle: RePEc:eee:apmaco:v:340:y:2019:i:c:p:1-4
    DOI: 10.1016/j.amc.2018.08.042
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    References listed on IDEAS

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    1. Cai, Qingqiong & Cao, Fuyuan & Li, Tao & Wang, Hua, 2018. "On distances in vertex-weighted trees," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 435-442.
    2. 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.
    3. Lan, Yongxin & Li, Tao & Ma, Yuede & Shi, Yongtang & Wang, Hua, 2018. "Vertex-based and edge-based centroids of graphs," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 445-456.
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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. Dobrynin, Andrey A. & Sharafdini, Reza, 2020. "Stepwise transmission irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    3. Bezhaev, Anatoly Yu. & Dobrynin, Andrey A., 2021. "On quartic transmission irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    4. 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.
    5. Al-Yakoob, Salem & Stevanović, Dragan, 2020. "On transmission irregular starlike trees," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    6. Andrey A. Dobrynin & Andrei Yu Vesnin, 2019. "On the Wiener Complexity and the Wiener Index of Fullerene Graphs," Mathematics, MDPI, vol. 7(11), pages 1-17, November.

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