| Title: | No-hole λ-L (k, k – 1, …, 2,1)-labeling for square grid |
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| Authors: | ID Atta, Soumen, Department of Computer Science and Engineering, University of Kalyani, Kalyani-741235, West Bengal, India (Author)
ID Goldstein, Stanisław, Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, PL-90-235 Lodz, Poland (Author)
ID Sinha Mahapatra, Priya Ranjan, Department of Computer Science and Engineering, University of Kalyani, Kalyani-741235, West Bengal, India (Author) |
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| Files: |
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | UNG - University of Nova Gorica
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| Abstract: | Motivated by a frequency assignment problem, we demonstrate, for a fixed positive integer k, how to label an infinite square grid with a possibly small number of integer labels, ranging from 0 to λ −1, in such a way that labels of adjacent vertices differ by at least k, vertices connected by a path of length two receive values which differ by at least k − 1, and so on. The vertices which are at least k + 1 distance apart may receive the same label. By finding a lower bound for λ, we prove that the solution is close to optimal, with approximation ratio at most 9/8. The labeling presented is a no-hole one, i.e., it uses each of the allowed labels at least once. |
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| Keywords: | graph labeling, labeling number, no-hole labeling, square grid, frequency assignment problem, approximation ratio |
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| Year of publishing: | 2017 |
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| Number of pages: | 9-19 |
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| Numbering: | 3, 63 |
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| PID: | 20.500.12556/RUNG-8150 |
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| COBISS.SI-ID: | 149321731 |
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| DOI: | 10.26485/0459-6854/2017/67.3/1 |
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| NUK URN: | URN:SI:UNG:REP:UJZTOZLJ |
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| Publication date in RUNG: | 17.04.2023 |
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| Views: | 1921 |
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| Downloads: | 0 |
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