$$L(j,k)$$ L ( j, k ) -labeling number of Cartesian product of path and cycle

Qiong Wu (), Wai Chee Shiu () and Pak Kiu Sun ()
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Qiong Wu: Hong Kong Baptist University
Wai Chee Shiu: Hong Kong Baptist University
Pak Kiu Sun: Hong Kong Baptist University

Journal of Combinatorial Optimization, 2016, vol. 31, issue 2, No 9, 604-634

Abstract: Abstract For positive numbers $$j$$ j and $$k$$ k , an $$L(j,k)$$ L ( j , k ) -labeling $$f$$ f of $$G$$ G is an assignment of numbers to vertices of $$G$$ G such that $$|f(u)-f(v)|\ge j$$ | f ( u ) - f ( v ) | ≥ j if $$d(u,v)=1$$ d ( u , v ) = 1 , and $$|f(u)-f(v)|\ge k$$ | f ( u ) - f ( v ) | ≥ k if $$d(u,v)=2$$ d ( u , v ) = 2 . The span of $$f$$ f is the difference between the maximum and the minimum numbers assigned by $$f$$ f . The $$L(j,k)$$ L ( j , k ) -labeling number of $$G$$ G , denoted by $$\lambda _{j,k}(G)$$ λ j , k ( G ) , is the minimum span over all $$L(j,k)$$ L ( j , k ) -labelings of $$G$$ G . In this article, we completely determine the $$L(j,k)$$ L ( j , k ) -labeling number ( $$2j\le k$$ 2 j ≤ k ) of the Cartesian product of path and cycle.

Keywords: $$L(j; k)$$ L ( j; k ) -labeling; Cartesian product; Path; Cycle; 05C78; 05C15 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-014-9775-4

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