Fuzzy fractional factors in fuzzy graphs
Wei Dong Gao, Weifan Wang, Lina Zheng · International Journal of Intelligent Systems · 2022
Graph fractional factor theory plays a crucial role in data transmission and network flow existence analysis, and has become one of the hot research branches of graph theory. This paper introduces fuzzy fractional factor in fuzzy graph setting, and an algorithm-based proof of its necessary and sufficient condition is given. The transformation operation is introduced to show that any two fuzzy fractional f $f$ -factors can be converted between each other, and the characteristic of maximum fuzzy fractional factor through increasing walk is determined. Finally, toughness in fuzzy graph setting is introduced, and preliminary toughness bound for fuzzy fractional ι $\iota $ -factor is presented, where ι = min e ∈ E { μ B ( e ) ∣ μ B ( e ) > 0 } $\iota ={\min }_{e\in E}\{{\mu }_{B}(e)| {\mu }_{B}(e)\gt 0\}$ .