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Note on (semi-)proper orientation of some triangulated planar graphs

Author

Listed:
  • Gu, Ruijuan
  • Lei, Hui
  • Ma, Yulai
  • Taoqiu, Zhenyu

Abstract

A weighted orientation of a graph G is a function (D, w) with an orientation D of G and with a weight function w:E(G)→Z+. The in-weightwD−(v) of a vertex v in D is the value Σu∈ND−(v)w(uv). A weighted orientation (D, w) of G is a semi-proper orientation if wD−(v)≠wD−(u) for all uv ∈ E(G). The semi-proper orientation number of G is defined as χ→s(G)=min(D,w)∈Γmaxv∈V(G)wD−(v), where Γ is the set of semi-proper orientations of G. When w(e)=1 for any e ∈ E(G), this parameter is equal to the proper orientation number of G.

Suggested Citation

  • Gu, Ruijuan & Lei, Hui & Ma, Yulai & Taoqiu, Zhenyu, 2021. "Note on (semi-)proper orientation of some triangulated planar graphs," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306767
    DOI: 10.1016/j.amc.2020.125723
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    Cited by:

    1. J. Ai & S. Gerke & G. Gutin & H. Lei & Y. Shi, 2023. "Proper orientation, proper biorientation and semi-proper orientation numbers of graphs," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-10, January.

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