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[1] Tao Fangyun, Gu Guohua, Xu Kexiang,. On L(2, 1)-labellings of distance graphs [J]. Journal of Southeast University (English Edition), 2005, 21 (2): 244-248. [doi:10.3969/j.issn.1003-7985.2005.02.026]
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On L(2, 1)-labellings of distance graphs()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
21
Issue:
2005 2
Page:
244-248
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2005-06-30

Info

Title:
On L(2, 1)-labellings of distance graphs
Author(s):
Tao Fangyun1;  Gu Guohua2;  Xu Kexiang3
1Department of Mathematics of College of Information Science and Technology, Nanjing Forest University, Nanjing 210037, China
2Department of Mathematics, Southeast University, Nanjing 210096, China
3College of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Keywords:
channel assignment problem;  L(2;  1)-labelling;  distance graphs
PACS:
O157.5
DOI:
10.3969/j.issn.1003-7985.2005.02.026
Abstract:
The L(2, 1)-labelling number of distance graphs G(D), denoted by λ(D), is studied.It is shown that distance graphs satisfy λ(G)≤Δ2.Moreover, we prove λ({1, 2, …, k})=2k+2 and λ({1, 3, …, 2k-1})=2k+2 for any fixed positive integer k.Suppose k, a∈N and k, a≥2.If k≥a, then λ({a, a+1, …, a+k-1})=2(a+k-1).Otherwise, λ({a, a+1, …, a+k-1})≤min{2(a+k-1), 6k-2}.When D consists of two positive integers, 6≤λ(D)≤8.For the special distance sets D={k, k+1}(∠k∈N), the upper bound of λ(D)is improved to 7.

References:

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Memo

Memo:
Biography: Tao Fangyun(1979—), female, master, winnietfy@sina.com.cn.
Last Update: 2005-06-20