| Title: | L (D, 2, 1)-labeling of Square Grid |
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| Authors: | ID Atta, Soumen, Department of Computer Science and Engineering, University of Kalyani, Kalyani, Nadia, West Bengal 741235, India (Author)
ID Sinha Mahapatra, Priya Ranjan, Department of Computer Science and Engineering, University of Kalyani, Kalyani, Nadia, West Bengal 741235, 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: | For a fixed integer $D (\geq 3)$ and $\lambda$ $\in$ $\mathbb{Z}^+$, a $\lambda$-$L(D, 2, 1)$-$labeling$ of a graph $G = (V, E)$ is the problem of assigning non-negative integers (known as labels) from the set $\{0, \ldots, \lambda\}$ to the vertices of $G$ such that if any two vertices in $V$ are one, two and three distance apart from each other then the assigned labels to these vertices must have a difference of at least $D$, 2 and 1 respectively. The vertices which are at least $4$ distance apart can receive the same label. The minimum value among all the possible values of $\lambda$ for which there exists a $\lambda$-$L(D, 2, 1)$-$labeling$ is known as the labeling number. In this paper $\lambda$-$L(D, 2 ,1)$-$labeling$ of square grid is considered. The lower bound on the labeling number for square grid is presented and a formula for $\lambda$-$L(D, 2 ,1)$-$labeling$ of square grid is proposed. The correctness proof of the proposed formula is given here. The upper bound of the labeling number obtained from the proposed labeling formula for square grid matches exactly with the lower bound of the labeling number. |
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| Keywords: | Graph labeling, Square grid, Labeling number, Frequency assignment problem (FAP) |
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| Year of publishing: | 2019 |
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| Number of pages: | 485-487 |
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| Numbering: | 6, 42 |
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| PID: | 20.500.12556/RUNG-8141 |
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| COBISS.SI-ID: | 149328643 |
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| DOI: | https://doi.org/10.1007/s40009-018-0780-5 |
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| NUK URN: | URN:SI:UNG:REP:VMO9ZZMV |
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| Publication date in RUNG: | 17.04.2023 |
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| Views: | 1503 |
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| Downloads: | 0 |
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