Schultz index S(G) = Σ (d(i)+d(j))·dist(i,j). Also known as Molecular Topological Index (MTI). Schultz (1989). Uses degree sum instead of product (cf. Gutman). For trees: S(T) = 4W(T) - n(n-1).
How to Use
Select graph:
- S: Schultz index
- (d+d)·dist: Per pair
- MTI: Molecular
MTI History
Schultz originally called it Molecular Topological Index. First degree-distance hybrid index. Inspired Gutman's product variant. Together they form the foundation of degree-distance indices.
Tree Formula
S(T) = 4W(T) - n(n-1). Surprisingly simple! For trees, S is essentially a shifted Wiener index. This means S and W are equivalent for ranking trees.
Step-by-Step Instructions
- 1Select graph.
- 2For each pair: (d(i)+d(j))·dist(i,j).
- 3Sum all terms.
- 4Check tree formula.
- 5Compare with Gutman.