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Stepwise irregular graphs

Author

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  • Gutman, Ivan

Abstract

A graph is stepwise irregular (SI) if the degrees of any two of its adjacent vertices differ by exactly one. Among graphs with non-zero edge imbalance, SI graphs are least irregular. Some basic properties of SI graphs are established.

Suggested Citation

  • Gutman, Ivan, 2018. "Stepwise irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 234-238.
    • Handle: RePEc:eee:apmaco:v:325:y:2018:i:c:p:234-238
    DOI: 10.1016/j.amc.2017.12.045
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    References listed on IDEAS

    as
    1. Chen, Xiaodan & Hou, Yaoping & Lin, Fenggen, 2018. "Some new spectral bounds for graph irregularity," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 331-340.
    2. Gutman, Ivan & Furtula, Boris & Das, Kinkar Ch., 2016. "On some degree-and-distance-based graph invariants of trees," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 1-6.
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    Cited by:

    1. Dobrynin, Andrey A. & Sharafdini, Reza, 2020. "Stepwise transmission irregular graphs," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    2. 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).
    3. Wei Gao & Muhammad Aamir & Zahid Iqbal & Muhammad Ishaq & Adnan Aslam, 2019. "On Irregularity Measures of Some Dendrimers Structures," Mathematics, MDPI, vol. 7(3), pages 1-15, March.
    4. Réti, Tamás, 2019. "On some properties of graph irregularity indices with a particular regard to the σ-index," Applied Mathematics and Computation, Elsevier, vol. 344, pages 107-115.

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