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用于通信信道分配的结构运算下的模糊关联着色

Fuzzy incidence coloring under structural operations for communication channel allocation.

作者信息

Deji Angmo, Wang Qian, Zhou Li

机构信息

Colleage of Mathematics and Computer Science, Northwest Minzu University, 730030, Lanzhou, China.

School of Computer Science and Information Security, Guilin University of Electronic Technology, 541000, Guilin, China.

出版信息

Sci Rep. 2025 Aug 6;15(1):28824. doi: 10.1038/s41598-025-13778-7.

DOI:10.1038/s41598-025-13778-7
PMID:40770016
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC12328833/
Abstract

Fuzzy incidence graphs (FIGs), as a significant extension of fuzzy graph (FG) theory, have been widely applied in modeling uncertainty within complex systems such as communication networks, transportation infrastructure, and distributed systems. A central concept in FIGs is fuzzy incidence coloring (FIC), which refers to assigning colors to fuzzy incidences such that adjacent fuzzy incidences receive distinct colors. The fuzzy incidence coloring number (FICN) represents the minimum number of colors required to achieve such a coloring. This paper focuses on the strong product (SP) operation of FIGs and systematically investigates the properties of the SP operation as well as the FICN of FIGs under such operations. The core contribution is the derivation of exact values of the FICN for SP graphs constructed from four fundamental types of FIGs: path, cycle, complete graphs, and star. To this end, we propose a dedicated algorithm, which is designed to efficiently compute the FICN of SP graphs. Finally, an application example on wireless channel allocation is presented to demonstrate the practical value of our research. By applying FICN, the minimum number of frequency signals required to avoid communication interference can be determined, thereby enabling optimized channel allocation, reduced interference, and improved communication management under constrained resources.

摘要

模糊关联图（FIGs）作为模糊图（FG）理论的重要扩展，已广泛应用于对通信网络、交通基础设施和分布式系统等复杂系统中的不确定性进行建模。FIGs中的一个核心概念是模糊关联着色（FIC），它是指为模糊关联分配颜色，使得相邻的模糊关联接收不同的颜色。模糊关联着色数（FICN）表示实现这种着色所需的最小颜色数。本文重点研究FIGs的强积（SP）运算，并系统地研究SP运算的性质以及在此类运算下FIGs的FICN。核心贡献是推导了由四种基本类型的FIGs（路径、圈、完全图和星）构造的SP图的FICN的精确值。为此，我们提出了一种专用算法，该算法旨在高效地计算SP图的FICN。最后，给出了一个无线信道分配的应用示例，以证明我们研究的实际价值。通过应用FICN，可以确定避免通信干扰所需的最小频率信号数，从而在资源受限的情况下实现优化的信道分配、减少干扰并改善通信管理。

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