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On interval transmission irregular graphs

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Abstract

Transmission of a vertex v of a connected graph G is the sum of distances from v to all other vertices in G. Graph G is transmission irregular (TI) if no two of its vertices have the same transmission, and G is interval transmission irregular (ITI) if it is TI and the vertex transmissions of G form a sequence of consecutive integers. Here we give a positive answer to the question of Dobrynin [Appl Math Comput 340 (2019), 1–4] of whether infinite families of ITI graphs exist.

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Acknowledgements

This work was supported and funded by Kuwait University Research Grant No. SM04/19

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Kuwait University, 13060, Safat, Kuwait

    Salem Al-Yakoob

  2. Mathematical Institute, Serbian Academy of Sciences and Arts, Kneza Mihaila 36, 11000, Belgrade, Serbia

    Dragan Stevanović

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  1. Salem Al-Yakoob
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  2. Dragan Stevanović
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Correspondence to Salem Al-Yakoob.

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This work was supported and funded by Kuwait University Research Grant No. SM04/19.

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Al-Yakoob, S., Stevanović, D. On interval transmission irregular graphs. J. Appl. Math. Comput. 68, 45–68 (2022). https://doi.org/10.1007/s12190-021-01513-0

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