Fuzzy incidence coloring under structural operations for communication channel allocation.

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.