-labeling of strong products of cycles

Korže, Danilo; Vesel, Aleksander

doi:10.1016/j.ipl.2005.01.007

Cited by 23 publications

(20 citation statements)

References 9 publications

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“…Since we have reduced the bound by . In [15] and [20], they obtained an upper bound for the -labeling number of the direct product of two graphs in terms of the maximum degrees of the graphs involved. We shall improve this bound.…”

Section: Resultsmentioning

confidence: 99%

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A New Approach to the $L(2,1)$-Labeling of Some Products of Graphs

Shiu

Shao

Poon

et al. 2008

IEEE Trans. Circuits Syst. II

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Abstract-The frequency assignment problem is to assign a frequency which is a nonnegative integer to each radio transmitter so that interfering transmitters are assigned frequencies whose separation is not in a set of disallowed separations. This frequency assignment problem can be modelled with vertex labelings of graphs. An ( 2 1 . In this paper, we develop a dramatically new approach on the analysis of the adjacency matrices of the graphs to estimate the upper bounds of -numbers of the four standard graph products. By the new approach, we can achieve more accurate results and with significant improvement of the previous bounds.Index Terms-Channel assignment, (2 1)-labeling, Cartesian product, lexicographic product, direct product, strong product.

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Section: Resultsmentioning

confidence: 99%

“…In [12] the -numbers of the strong product of cycles are considered. In [15] and [20], they obtained a general upper bound for the -number of strong products in terms of maximum degrees of the factor graphs (and the product).…”

Section: Resultsmentioning

confidence: 99%

A New Approach to the $L(2,1)$-Labeling of Some Products of Graphs

Shiu

Shao

Poon

et al. 2008

IEEE Trans. Circuits Syst. II

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show abstract

“…Therefore, we assume and . In [13] and [16], the -numbers of the strong product of cycles are considered. In this section, we obtain a general upper bound for the -number of strong products in terms of maximum degrees of the factor graphs (and the product).…”

Section: Strong Product Of Graphsmentioning

confidence: 99%

Improved Bounds on the $L(2,1)$-Number of Direct and Strong Products of Graphs

Shao

Klavžar

Shiu

et al. 2008

IEEE Trans. Circuits Syst. II

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Abstract-The frequency assignment problem is to assign a frequency which is a nonnegative integer to each radio transmitter so that interfering transmitters are assigned frequencies whose separation is not in a set of disallowed separations. This frequency assignment problem can be modelled with vertex labelings of graphs. An (2 1)-labeling of a graph is a function from the vertex set ( ) to the set of all nonnegative integers such that ( ) . This paper considers the graph formed by the direct product and the strong product of two graphs and gets better bounds than those of Klavžar andŠpacapan with refined approaches.

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“…So it is not possible to compute λ-number of a graph in polynomial time unless P = NP. Therefore, the problem has been studied for many special classes of graphs, such as regular grids [1,2], product graphs [10,14], trees [4,18], planar graphs [17], generalized flowers [11], permutation and bipartite permutation graphs [15] and so on. For more details, one may refer to the surveys [3,19].…”

Section: Introductionmentioning

confidence: 99%

Distance Two Labeling on the Square of a Cycle

ZHANG

2015

Korean Journal of Mathematics

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Abstract. An L(2, 1)-labeling of a graph G is a function f from the vertex set V (G) to the set of all non-negative integers such thatThe λ-number of G, denoted λ(G), is the smallest number k such that G admits an L(2, 1)-labeling with k = max{f (u)|u ∈ V (G)}. In this paper, we consider the square of a cycle and provide exact value for its λ-number. In addition, we also completely determine its edge span.

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-labeling of strong products of cycles

Cited by 23 publications

References 9 publications

A New Approach to the $L(2,1)$-Labeling of Some Products of Graphs

A New Approach to the $L(2,1)$-Labeling of Some Products of Graphs

Improved Bounds on the $L(2,1)$-Number of Direct and Strong Products of Graphs

Distance Two Labeling on the Square of a Cycle

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