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.

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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, Vicky
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
1872-6771
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
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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