Circular L(j,k)-labeling number of direct product of path and cycle

Wu, Qiong; Shiu, Wai Chee; Sun, Pak Kiu

doi:10.1007/s10878-012-9520-9

Cited by 13 publications

(5 citation statements)

References 13 publications

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“…For instance, Wu and Lin [10] introduced the circular L(j, k)-labeling numbers of trees and products of graphs. Wu, Shiu and Sun [11] determined the circular L(j, k)-labeling numbers of direct product of path and cycle. Furthermore, Wu and Shiu [12] investigated the circular L(j, k)-labeling numbers of square of paths.…”

Section: Introductionmentioning

confidence: 99%

Circular L(j,k)-Labeling Numbers of Cartesian Product of Three Paths

Rao

2022

Proceeding of 2021 International Conference on Wireless Communications, Networking and Applications

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The circular $$L(j,k)$$ L ( j , k ) -labeling problem with $$k\ge j$$ k ≥ j arose from the code assignment in the wireless network of computers. Given a graph $$G$$ G and positive numbers $$j,k,\sigma $$ j , k , σ , and a circular $$\sigma $$ σ -$$L(j,k)$$ L ( j , k ) -labeling of a graph $$G$$ G is an assignment $$f$$ f from $$[0,\sigma )$$ [ 0 , σ ) to the vertices of $$G$$ G , for any two vertices $$u$$ u and $$v$$ v , such that $$|f(u)-f(v){|}_{\sigma }\ge j$$ | f ( u ) - f ( v ) | σ ≥ j if $$uv\in E(G)$$ u v ∈ E ( G ) , and $$|f(u)-f(v){|}_{\sigma }\ge k$$ | f ( u ) - f ( v ) | σ ≥ k if $$u$$ u and $$v$$ v are distance two apart, where $$|f\left(u\right)-f\left(v\right){|}_{\sigma }=min\left\{|f(u)-f(v)|, \sigma -|f(u)-f(v)|\right\}$$ | f u - f v | σ = m i n | f ( u ) - f ( v ) | , σ - | f ( u ) - f ( v ) | . The minimum $$\sigma $$ σ such that graph $$G$$ G has a circular $$\sigma $$ σ -$$L(j,k)$$ L ( j , k ) -labeling of a graph $$G$$ G , which is called the circular $$L(j,k)$$ L ( j , k ) -labeling number of graph $$G$$ G and is denoted by $${\sigma }_{j,k}(G)$$ σ j , k ( G ) . In this paper, we determine the circular $$L(j,k)$$ L ( j , k ) -labeling numbers of Cartesian product of three paths, where $$k\ge 2j.$$ k ≥ 2 j .

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Section: Introductionmentioning

confidence: 99%

Circular L(j,k)-Labeling Numbers of Cartesian Product of Three Paths

Rao

2022

Proceeding of 2021 International Conference on Wireless Communications, Networking and Applications

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“…Recently, Shiu and Wu determined L(1, d)-labeling numbers of square of paths in [10]. Moreover, the authors also introduced some L(1, d)-labeling numbers of graphs in [9,[11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

L(1, 2)-labeling numbers on square of cycles

Liu

2020

AKCE International Journal of Graphs and Combinatorics

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For two positive numbers d and m, an m-L(1, d)-labeling of a graph G is a mapping f : VðGÞ ! ½0, m such that jf ðuÞ À f ðvÞj ! 1 if dðu, vÞ ¼ 1, and jf ðuÞ À f ðvÞj ! d if dðu, vÞ ¼ 2: The span of f is the maximum difference among the numbers assigned by f. The L(1, d)-labeling number of G, denoted by k 1, d ðGÞ, is the minimum span over all L(1, d)-labelings of G. In this paper, we determine the L(1, 2)-labeling numbers of square of cycles C n for all values n.

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“…For surveys of the λ h,k (G)-labelling problem, including λ-number of graphs, see [2,3,19]. Recently, there are some results on L(h, k) labelling problem [5,15] and some interesting generalizations, like multiple labelling and circular labelling, of graphs [14,18,20].…”

Section: Introductionmentioning

confidence: 99%

L(h,k)-labelling for octagonal grid

Kim

Rho

Song

2014

International Journal of Computer Mathematics

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An L(h, k)-labelling of a graph G is an assignment of nonnegative integers, called labels, to the vertices of G such that two adjacent vertices receive labels that differ by at least h and those of distance two receive labels that differ by at least k. Among the span of all L(h, k)-labellings of G, λ h,k (G) is the smallest one. In this paper for the octagonal grid G 8 , we show that the upper bound for λ h,k (G 8 ) is 3h + 6k when h ≥ 4k. And when h > 6k, we show that λ h,k (G 8 ) = 3h + 6k.

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Circular L(j,k)-labeling number of direct product of path and cycle

Cited by 13 publications

References 13 publications

Circular L(j,k)-Labeling Numbers of Cartesian Product of Three Paths

Circular L(j,k)-Labeling Numbers of Cartesian Product of Three Paths

L(1, 2)-labeling numbers on square of cycles

L(h,k)-labelling for octagonal grid

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