On L(d,1)-labelings of graphs

Distance constrained labeling problems, e.g., L(p, q)-labeling and (p, q)-total labeling, are originally motivated by the frequency assignment. From the viewpoint of theory, the upper bounds on the labeling numbers and the time complexity of finding a minimum labeling are intensively and extensively studied. In this paper, we survey the distance constrained labeling problems from algorithmic aspects, that is, computational complexity, approximability, exact computation, and so on.

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“…2,1 n) time [15]. Both results are based on Chang and Kuo's algorithm, which is called as a subroutine in the algorithms.…”

Section: L(2 1)-labeling Problemmentioning

confidence: 99%

Algorithmic aspects of distance constrained labeling: a survey

Hasunuma

Ishii

Ono

et al. 2014

IJNC

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“…L -labeling has been extensively studied in recent past by many researchers [see 2,5,9,10,12,13,20]. The common trend in most of the research paper is either to determine the value of (2,1) L -labeling number or to suggest bounds for particular classes of graphs.…”

Section: Introductionmentioning

confidence: 99%

The L(2,1) -Labelings on the Homomorphic Product of two Graphs

2017

IJCSI

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“…The ( ) L p q -labelling of graphs have been studied rather extensively in recent years [2,3,4,5,6].…”

Section: Introductionmentioning

confidence: 99%

The research of (2,1)-total labelling of trees basen on Frequency Channel Assignment problem

Sun

2015

MATEC Web of Conferences

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Abstract. Let T be a tree, Let DΔ (T) denote the set of integers k for which there exist two distinct vertices of maximum degree of distance at k in T. The (2,1)-total labelling number of a graph G is the width of the smallest range of integers that suffices to label the vertices and the edges of G such that no two adjacent vertices have the same label, no two adjacent edges have the same label and the difference between the labels of a vertex and its incident edges is at least 2. In this paper, we prove that if T is a tree with Δ≥5 and 3 4 ( ) D T ' , then T is Type 1.

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On L(d,1)-labelings of graphs

Cited by 120 publications

References 10 publications

Algorithmic aspects of distance constrained labeling: a survey

Algorithmic aspects of distance constrained labeling: a survey

The L(2,1) -Labelings on the Homomorphic Product of two Graphs

The research of (2,1)-total labelling of trees basen on Frequency Channel Assignment problem

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