For any abstract elliptic operator on a closed, oriented, topological manifold, the analytical index equals the topological index.

For a school district with a market value/personal income aid ratio (MV/PI AR) greater than 0.4000, its index equals the base index multiplied by the sum of .75 and its MV/PI AR for the current year.

Another theorem about bipartite graphs, that their chromatic index equals their maximum degree, is equivalent to the perfection of the line graphs of bipartite graphs.

The index (the n) equals to the number of nodes in the diagram, the number of simple roots in a basis, the dimension of the root lattice and span of the root system, the number of generators of the Coxeter group, and the rank of the Lie algebra.

The original Simpson's index hence equals the corresponding basic sum.

Now König's Line Coloring Theorem, stating that the chromatic index equals the maximum vertex degree in any bipartite graph, can be interpreted as stating that the line graph of a bipartite graph is perfect.