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On the maximum size of stepwise irregular graphs

Author

Listed:
  • Buyantogtokh, Lkhagva
  • Azjargal, Enkhbayar
  • Horoldagva, Batmend
  • Dorjsembe, Shiikhar
  • Adiyanyam, Damchaa

Abstract

Recently, Gutman introduced the class of stepwise irregular graphs and studied their properties. A graph is stepwise irregular if the difference between the degrees of any two adjacent vertices is exactly one. In this paper, we get some upper bounds on the maximum degree and sharp upper bounds on the size of stepwise irregular graphs. Furthermore, we completely characterize the graphs with maximum size among all connected stepwise irregular graphs of the given order.

Suggested Citation

  • Buyantogtokh, Lkhagva & Azjargal, Enkhbayar & Horoldagva, Batmend & Dorjsembe, Shiikhar & Adiyanyam, Damchaa, 2021. "On the maximum size of stepwise irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306366
    DOI: 10.1016/j.amc.2020.125683
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    References listed on IDEAS

    as
    1. Deng, Kecai & Li, Shuchao, 2021. "On the extremal values for the Mostar index of trees with given degree sequence," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    2. Gutman, Ivan, 2018. "Stepwise irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 234-238.
    3. Abdo, Hosam & Dimitrov, Darko & Gutman, Ivan, 2019. "Graph irregularity and its measures," Applied Mathematics and Computation, Elsevier, vol. 357(C), pages 317-324.
    4. Tepeh, Aleksandra, 2019. "Extremal bicyclic graphs with respect to Mostar index," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 319-324.
    Full references (including those not matched with items on IDEAS)

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