| Title: | Optimal L(d,1)-Labeling of Certain Direct Graph Bundles Cycles over Cycles and Cartesian Graph Bundles Cycles over Cycles |
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| Authors: | ID Hrastnik Ladinek, Irena, Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia (Author) |
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| Files: |  mathematics-12-03121-v2.pdf (338,54 KB)
MD5: E2C87FFDF4798C5A8C4E7C30163D8C22
 https://www.mdpi.com/2227-7390/12/19/3121
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FS - Faculty of Mechanical Engineering
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| Abstract: | An L(d,1)-labeling of a graph G=(V,E) is a function f from the vertex set V(G) to the set of nonnegative integers such that the labels on adjacent vertices differ by at least d and the labels on vertices at distance two differ by at least one, where d≥1. The span of f is the difference between the largest and the smallest numbers in f(V). The λ1d-number of G, denoted by λ1d(G), is the minimum span over all L(d,1)-labelings of G. We prove that λ1d(X)≤2d+2, with equality if 1≤d≤4, for direct graph bundle X=Cm×σℓCn and Cartesian graph bundle X=Cm□σℓCn, if certain conditions are imposed on the lengths of the cycles and on the cyclic ℓ-shift σℓ.
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| Keywords: | L(d, 1)-labeling, λ d 1 -number, direct product of graph, direct graph bundle, Cartesian product of graph, Cartesian graph bundle, cyclic ℓ-shift, channel assignment |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 02.09.2024 |
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| Article acceptance date: | 04.10.2024 |
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| Publication date: | 05.10.2024 |
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| Publisher: | MDPI AG |
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| Year of publishing: | 2024 |
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| Number of pages: | str. 3121 |
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| Numbering: | Vol. 12, no. 19 |
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| PID: | 20.500.12556/DKUM-92050  |
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| UDC: | 519.17 |
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| eISSN: | 2227-7390 |
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| COBISS.SI-ID: | 214025731 |
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| DOI: | https://dx.doi.org/10.3390/math12193121 |
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| Copyright: | © 2024 by the author |
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| Publication date in DKUM: | 13.03.2025 |
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| Views: | 150 |
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| Downloads: | 15 |
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| Metadata: |    |
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| Categories: | Misc.
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