Fibonacci range labeling for shell–flower related graphs
Aronthung S Odyuo, P. Mercy, Manoj Kumar Patel · 2023
Fibonacci range labeling of a graph is an injective function f : V(G) → {f2, f3, f4, . . . , fe+1} such that when each edge e = (α, β) is labeled with f ∗(e = αβ) = ⌈ f (α)2+f (β)2 f (α)+f (β) ⌉ or f ∗(e = αβ) = ⌊ f (α)2+f (β)2 f (α)+f (β) ⌋, then the resulting edge gets unique label. Also, the ratio of each edge to the preceding edge is in the form of the golden ratio given by Rt(Ei,i+1) = Ei+1 Ei ≈ ψ (for larger i), where Rt(Ei,i+1) is the ratio of the resulting induced edge, and ψ = 1.618 is known as the golden ratio.