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Open Access Research Article

L(1, d)-labeling number of direct product of two cycles

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pp. 2097–2125Vol. 26Issue 8December 2023DOI: 10.1080/09720529.2021.1930652 Crossmark XML
Received:
01 Nov 2020
Accepted:
01 Mar 2021
Published Online:
24 May 2022
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-1352
Pages:
2097–2125

Abstract

For positive number d, an L(1, d) -labeling f of G is an assignment of numbers to vertices of G such that |f(u) - f(v)| ≥ 1 if d(u, v) = 1, and |f(u) - f(v)| ≥ d if d(u, v) = 2. Then the span of f is the difference between the maximum and the minimum numbers assigned by f. The L(1, d) -labeling number of G, denoted by λ1,d (G), is the minimum span over all L(1, d) -labelings of G. In this paper, the authors give the L(1, d) -labeling numbers of the direct product of two cycles Cm and Cn for d ≥ 2 for some values of m and n. Some cases for 1 ≤ d <2 are also discussed.

Keywords

Subject Classifications

(2010) 05C7805C15

References

[1] N. Abrahmson, The ALOHA system-Another alternative for computer communications, Proc. FJCC, (1970), 281-285.
[2] A.A. Bertossi and M.A. Bonuccelli, Code assignment for hidden terminal interference avoidance in multihop packet radio networks, IEEE/ACM Transtractions on Networking, 3(4) (1995), 441–449.
[3] J.A. Bondy, U.S.R. Murty, Graph theory with applications, New York, MacMillan, 1976.
[4] T. Calamoneri, A. Pelc, and R. Petreschi, Labeling trees with a condition at distance two, Discrete Math., 306 (2006), 1534–1539.
[5] X.T. Jin and R.K. Yeh, Graph distance-dependent labeling related to code assignment in computer networks, Naval Research Logistics, 52 (2005) , 159–164.
[6] Q. Niu, (,)Ljk-labeling of graph and edge span, M.Phil. Thesis, Southeast University, 2007.
[7] W.C. Shiu and Q. Wu, (,)Ljk-labeling number of direct product of path and cycle, Acta Math. Sinica, 29 (2013), 1437–1448.
[8] Q. Wu and W. Lin, Circular (,)Ljk-labeling numbers of trees and products of graphs, J. Southeast University, 26(1) (2010),142-145.
[9] Q. Wu and W.C. Shiu, Circular L(j,k)-labeling number of square of paths, J. Combin. Number Theory, 9(1)(2017), 41–46.
[10] Q. Wu and W.C. Shiu, L(j,k)-labeling number of square of paths, AKCE International Journal of Graphs and Combinatorics, 14(3) (2017), 307–316.
[11] Q. Wu, W.C. Shiu and P.K. Sun, L(j,k)-labeling number of Cartesian product of path and cycle, J. Combin. Optimization, 31 (2016), 604–634.
[12] Q. Wu, W.C. Shiu and P.K. Sun, Circular L(j,k)-labeling number of direct product of path and cycle, J. Combin. Optimization, 27(2014), 355–368 .

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