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<p>In wireless telecommunication networks, where a multitude of communication links exist but only a restricted number of frequencies are available, the challenge of strategically assigning these frequencies to transmitters to minimize interference is known as the frequency allocation problem. This problem is commonly represented and approached through the lens of graph <i>L</i>(2,&#xa0;1)-coloring, a recognized methodology for resolving such allocation challenges. In this paper, we consider frequency allocation as a graph <i>L</i>(2,&#xa0;1)-coloring problem over an algebraic structure, a ring <i>R</i> with unity 1 not equal to zero. In <i>L</i>(2,&#xa0;1)-coloring model of a network adjacent transceivers situated in very close proximity are assigned frequencies with a minimum difference of two. Meanwhile, transceivers in close vicinity are assigned frequencies that differ by at least one. This coloring scheme ensures effective frequency allocation while managing interference in wireless communication networks.</p>

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Frequency allocation problem over an algebraic structure

  • 期刊论文

  • 发表日期：

    2025年5月29日

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  • Annayat Ali,
  • Rameez Raja

摘要

In wireless telecommunication networks, where a multitude of communication links exist but only a restricted number of frequencies are available, the challenge of strategically assigning these frequencies to transmitters to minimize interference is known as the frequency allocation problem. This problem is commonly represented and approached through the lens of graph L(2, 1)-coloring, a recognized methodology for resolving such allocation challenges. In this paper, we consider frequency allocation as a graph L(2, 1)-coloring problem over an algebraic structure, a ring R with unity 1 not equal to zero. In L(2, 1)-coloring model of a network adjacent transceivers situated in very close proximity are assigned frequencies with a minimum difference of two. Meanwhile, transceivers in close vicinity are assigned frequencies that differ by at least one. This coloring scheme ensures effective frequency allocation while managing interference in wireless communication networks.