Hosoya index Z(G): total number of matchings (independent edge sets), including empty. Hosoya (1971): the first topological index ever proposed! Z(P_n) = F(n+1) (Fibonacci!). Correlates with boiling point, entropy, heat of formation.
How to Use
Select graph:
- Z: Hosoya index
- m(k): k-matchings
- Fib: Path = Fibonacci
Fibonacci Connection
Z(P_n) = F(n+1): Hosoya index of a path is Fibonacci! P₁:1, P₂:2, P₃:3, P₄:5, P₅:8, .... Also: Z(C_n) = L(n) (Lucas numbers). Beautiful combinatorial identities.
Chemical Applications
First topological index (1971). Z correlates with: boiling point (alkanes), acentric factor, entropy, heat of vaporization. Large Z → more matchings → more complex bonding → higher boiling point.
Step-by-Step Instructions
- 1Select graph.
- 2Count all matchings.
- 3Sum m(0)+m(1)+...+m(ν).
- 4Check Fibonacci.
- 5Compare molecules.