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Fuzzy incidence coloring under structural operations for communication channel allocation.

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Summary

This study determines the fuzzy incidence coloring number (FICN) for strong product fuzzy incidence graphs (FIGs). The research provides exact FICN values for key graph types and an algorithm for efficient computation, aiding wireless channel allocation.

Keywords:
Chromatic numberFuzzy incidence graphOperations of fuzzy incidence graphsProducts of fuzzy incidence graphs

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Area of Science:

  • Graph Theory
  • Fuzzy Mathematics
  • Discrete Mathematics

Background:

  • Fuzzy Incidence Graphs (FIGs) extend fuzzy graph theory for complex systems.
  • Fuzzy Incidence Coloring (FIC) assigns colors to fuzzy incidences, with the Fuzzy Incidence Coloring Number (FICN) being the minimum colors needed.
  • Understanding FICN is crucial for applications involving uncertainty and resource allocation.

Purpose of the Study:

  • Investigate the properties of the strong product (SP) operation on FIGs.
  • Derive exact FICN values for SP graphs of fundamental FIG types (path, cycle, complete, star).
  • Develop an efficient algorithm for computing the FICN of SP graphs.

Main Methods:

  • Systematic analysis of the strong product operation on FIGs.
  • Derivation of mathematical formulas for FICN on specific SP graph structures.
  • Development and application of a dedicated algorithm for FICN computation.

Main Results:

  • Exact FICN values were derived for strong products of path, cycle, complete, and star fuzzy incidence graphs.
  • A novel algorithm was proposed for efficiently computing the FICN of these SP graphs.
  • The practical utility of FICN was demonstrated through a wireless channel allocation example.

Conclusions:

  • The study successfully characterized the FICN of strong product fuzzy incidence graphs.
  • The developed algorithm provides an efficient tool for calculating FICN.
  • The findings offer a robust method for optimizing resource allocation in communication systems.