$$L(1,1)$$ L ( 1, 1 ) -labelling of the direct product of a complete graph and a cycle

Byeong Moon Kim (), Yoomi Rho () and Byung Chul Song ()
Additional contact information
Byeong Moon Kim: Gangneung-Wonju National University
Yoomi Rho: University of Incheon
Byung Chul Song: Gangneung-Wonju National University

Journal of Combinatorial Optimization, 2015, vol. 30, issue 3, No 23, 803-811

Abstract: Abstract An $$L(j,k)$$ L ( j , k ) -labeling of a graph is a vertex labeling such that the difference of the labels of any two adjacent vertices is at least $$j$$ j and that of any two vertices of distance $$2$$ 2 is at least $$k$$ k . The minimum span of all $$L(j,k)$$ L ( j , k ) -labelings of $$G$$ G is denoted by $$\lambda _k^j(G)$$ λ k j ( G ) . Lin and Lam (Discret Math 308:3805–3815, 2008) provided an upper bound of $$\lambda _1^2(K_m \times C_n)$$ λ 1 2 ( K m × C n ) when $$K_m \times C_n$$ K m × C n is the direct product of a complete graph $$K_m$$ K m and a cycle $$C_n$$ C n . And they found the exact value of $$\lambda _1^2(K_m \times C_n)$$ λ 1 2 ( K m × C n ) for some $$m$$ m and $$n$$ n . In this paper, we obtain an upper bound and a lower bound of $$\lambda _1^1(K_m \times C_n)$$ λ 1 1 ( K m × C n ) . As a consequence we compute $$\lambda _1^1(K_m \times C_n)$$ λ 1 1 ( K m × C n ) when $$n$$ n is even or $$n\ge 4m+1$$ n ≥ 4 m + 1 .

Keywords: L(1; 1)-labeling; Channel assignment problem; Direct product; Complete graph; Cycle; Kneser graph; 05C38; 05C78 (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-013-9669-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:30:y:2015:i:3:d:10.1007_s10878-013-9669-x

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-013-9669-x

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().