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

Ruijuan Gu, Hui Lei, Yulai Ma and Zhenyu Taoqiu

Applied Mathematics and Computation, 2021, vol. 392, issue C

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.

Keywords: Proper orientation number; Semi-proper orientation number; Triangulated planar graph (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300320306767
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306767

DOI: 10.1016/j.amc.2020.125723

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().