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Optimal Radio Labeling of Cartesian Product of Wheel Graph and Cycle.

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Title: Optimal Radio Labeling of Cartesian Product of Wheel Graph and Cycle.
Authors: Zhixuan Zhang1 zzxuan1208@163.com, Feng Li2 li2006369@126.com
Source: IAENG International Journal of Applied Mathematics. Jan2026, Vol. 56 Issue 1, p188-196. 9p.
Subjects: Graph theory, Spectrum allocation, Resource allocation, Data transmission systems, Systems design, Mathematical optimization
Abstract: Rapid advances in wireless communication have led to significant improvements in data transmission speeds, network coverage, and other aspects. However, the scarcity of spectrum resources presents a substantial challenge in modern network design. To address this issue, we transform the network frequency assignment problem into a graph vertex labeling and optimization problem. By introducing distance constraints on labeling and assigning unique labels to each site based on the spatial distribution of network nodes, we construct a spectrum assignment scheme that enhances the efficiency of spectrum management. This approach effectively improves the utilization of limited spectrum resources. In this paper, we focus on the radio labeling problem of the Cartesian product of the m-vertex wheel graph Wm and the n-vertex cycle Cn, where m ≥ 3 and n≥4. By exploring the conditions satisfied by the radio labeling problem for such special graph, we present relevant theorems and examples. Corresponding comparative experiments are also provided to validate the effectiveness of the network model proposed in this paper. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Optimal Radio Labeling of Cartesian Product of Wheel Graph and Cycle.
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  Data: <searchLink fieldCode="AR" term="%22Zhixuan+Zhang%22">Zhixuan Zhang</searchLink><relatesTo>1</relatesTo><i> zzxuan1208@163.com</i><br /><searchLink fieldCode="AR" term="%22Feng+Li%22">Feng Li</searchLink><relatesTo>2</relatesTo><i> li2006369@126.com</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Jan2026, Vol. 56 Issue 1, p188-196. 9p.
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  Data: <searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Spectrum+allocation%22">Spectrum allocation</searchLink><br /><searchLink fieldCode="DE" term="%22Resource+allocation%22">Resource allocation</searchLink><br /><searchLink fieldCode="DE" term="%22Data+transmission+systems%22">Data transmission systems</searchLink><br /><searchLink fieldCode="DE" term="%22Systems+design%22">Systems design</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Rapid advances in wireless communication have led to significant improvements in data transmission speeds, network coverage, and other aspects. However, the scarcity of spectrum resources presents a substantial challenge in modern network design. To address this issue, we transform the network frequency assignment problem into a graph vertex labeling and optimization problem. By introducing distance constraints on labeling and assigning unique labels to each site based on the spatial distribution of network nodes, we construct a spectrum assignment scheme that enhances the efficiency of spectrum management. This approach effectively improves the utilization of limited spectrum resources. In this paper, we focus on the radio labeling problem of the Cartesian product of the m-vertex wheel graph Wm and the n-vertex cycle Cn, where m ≥ 3 and n≥4. By exploring the conditions satisfied by the radio labeling problem for such special graph, we present relevant theorems and examples. Corresponding comparative experiments are also provided to validate the effectiveness of the network model proposed in this paper. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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        PageCount: 9
        StartPage: 188
    Subjects:
      – SubjectFull: Graph theory
        Type: general
      – SubjectFull: Spectrum allocation
        Type: general
      – SubjectFull: Resource allocation
        Type: general
      – SubjectFull: Data transmission systems
        Type: general
      – SubjectFull: Systems design
        Type: general
      – SubjectFull: Mathematical optimization
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      – TitleFull: Optimal Radio Labeling of Cartesian Product of Wheel Graph and Cycle.
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              Text: Jan2026
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              Y: 2026
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