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Distance-unbalancedness of graphs

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  • Miklavič, Štefko
  • Šparl, Primož

Abstract

In this paper we propose and study a new structural invariant for graphs, called distance-unbalancedness, as a measure of how much a graph is (un)balanced in terms of distances. Explicit formulas are presented for several classes of well-known graphs. Distance-unbalancedness of trees is also studied. A few conjectures are stated and some open problems are proposed.

Suggested Citation

  • Miklavič, Štefko & Šparl, Primož, 2021. "Distance-unbalancedness of graphs," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    • Handle: RePEc:eee:apmaco:v:405:y:2021:i:c:s0096300321003234
    DOI: 10.1016/j.amc.2021.126233
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    References listed on IDEAS

    as
    1. Bessy, Stéphane & Dross, François & Hriňáková, Katarína & Knor, Martin & Škrekovski, Riste, 2020. "Maximal Wiener index for graphs with prescribed number of blocks," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    2. Knor, Martin & Škrekovski, Riste & Tepeh, Aleksandra, 2019. "Trees with the maximal value of Graovac–Pisanski index," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 287-292.
    3. Xu, Kexiang & Gu, Xiaoqian & Gutman, Ivan, 2018. "Relations between total irregularity and non-self-centrality of graphs," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 461-468.
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