[1] He Dan, Lin Wensong,. L(1, 2)-edge-labeling for necklaces [J]. Journal of Southeast University (English Edition), 2014, 30 (4): 550-554. [doi:10.3969/j.issn.1003-7985.2014.04.025]

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

30

Issue:

2014 4

Page:

550-554

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2014-12-31

Info

Title:

L(1, 2)-edge-labeling for necklaces

Author(s):

He Dan;  Lin Wensong

Department of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

channel assignment;  L(j;  k)-edge-labeling;  Cartesian product;  Halin graph;  necklace

PACS:

O157.5

DOI:

10.3969/j.issn.1003-7985.2014.04.025

Abstract:

For a graph G and two positive integers j and k, an m-L(j, k)-edge-labeling of G is an assignment from the set {0, 1, …, m} to the edges, such that adjacent edges receive labels that differ by at least j, and edges at distance two receive labels that differ by at least k. The λ′_{j, k}-number of G, denoted by λ′_{j, k}(G), is the minimum integer m overall m-L(j, k)-edge-labeling of G. The necklace is a specific type of Halin graph. The L(1, 2)-edge-labeling of necklaces is studied and the lower and upper bounds on λ′_{1, 2}-number for necklaces are given. Also, both the lower and upper bounds are attainable.

References:

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Memo

Memo:

Biographies: He Dan(1977—), female, graduate; Lin Wensong(corresponding author), male, doctor, professor, wslin@seu.edu.cn.
Foundation item: The National Natural Science Foundation of China(No.10971025, 10901035).
Citation: He Dan, Lin Wensong.L(1, 2)-edge-labeling for necklaces[J].Journal of Southeast University(English Edition), 2014, 30(4):550-554.[doi:10.3969/j.issn.1003-7985.2014.04.025]

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