Optimal radio labellings of complete m-ary trees

Li, Xiangwen, Mak, Vicky and Zhou, Sanming 2010, Optimal radio labellings of complete m-ary trees, Discrete applied mathematics, vol. 158, no. 5, pp. 507-515, doi: 10.1016/j.dam.2009.11.014.

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Title Optimal radio labellings of complete m-ary trees
Formatted title Optimal radio labellings of complete m-ary trees
Author(s) Li, Xiangwen
Mak, VickyORCID iD for Mak, Vicky orcid.org/0000-0002-9306-5780
Zhou, Sanming
Journal name Discrete applied mathematics
Volume number 158
Issue number 5
Start page 507
End page 515
Total pages 9
Publisher Elsevier BV
Place of publication Amsterdam, Netherlands
Publication date 2010-03-06
ISSN 0166-218X
Summary A radio labelling of a connected graph G is a mapping f : V (G) → {0, 1, 2, ...} such that | f (u) - f (v) | ≥ diam (G) - d (u, v) + 1 for each pair of distinct vertices u, v ∈ V (G), where diam (G) is the diameter of G and d (u, v) the distance between u and v. The span of f is defined as maxu, v V (G) | f (u) - f (v) |, and the radio number of G is the minimum span of a radio labelling of G. A complete m-ary tree (m ≥ 2) is a rooted tree such that each vertex of degree greater than one has exactly m children and all degree-one vertices are of equal distance (height) to the root. In this paper we determine the radio number of the complete m-ary tree for any m ≥ 2 with any height and construct explicitly an optimal radio labelling.
Language eng
DOI 10.1016/j.dam.2009.11.014
Field of Research 010303 Optimisation
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
HERDC collection year 2010
Copyright notice ©2009, Elsevier B.V. All rights reserved.
Persistent URL http://hdl.handle.net/10536/DRO/DU:30033648

Document type: Journal Article
Collection: School of Information Technology
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