Topological Index

In general, a topological index, sometimes also known as a graph-theoretic index, is a numerical invariant of a chemical graph (Plavšić et al. 1993). Particular topological indices include the Balaban index, Harary index, molecular topological index, and Wiener index. Unless otherwise stated, hydrogen atoms are usually ignored in the computation of such indices as organic chemists usually do when they write a benzene ring as a hexagon (Devillers and Balaban 1999, p. 25).

"The" topological index of a graph index defined by


where A is the adjacency matrix, D is the graph distance matrix, and |A+D| denotes the determinant of the matrix addition (Devillers and Balaban 1999, p. 31).

Precomputed values of the topological index for common graphs are implemented in the Wolfram Language as GraphData[graph, "TopologicalIndex"].

See also

Adjacency Matrix, Balaban Index, Graph Distance Matrix, Harary Index, Hosoya Index, Molecular Topological Index, Wiener Index

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Devillers, J. and Balaban, A. T. (Eds.). Topological Indices and Related Descriptors in QSAR and QSPR. Amsterdam, Netherlands: Gordon and Breach, p. 31, 1999.Plavšić, D.; Nikolić, S.; Trinajstić, N.; and Mihalić, Z. "On the Harary Index for the Characterization of Chemical Graphs." J. Math. Chem. 12, 235-250, 1993.Schultz, H. P. "Topological Organic Chemistry. 1. Graph Theory and Topological Indices of Alkanes." J. Chem. Inf. Comput. Sci. 29, 227-228, 1989.Schultz, H. P.; Schultz, E. B.; and Schultz, T. P. "Topological Organic Chemistry. Part 2. Graph Theory, Matrix Determinants and Eigenvalues, and Topological Indices of Alkanes." J. Chem. Inf. Comput. Sci. 30, 27-29, 1990.

Referenced on Wolfram|Alpha

Topological Index

Cite this as:

Weisstein, Eric W. "Topological Index." From MathWorld--A Wolfram Web Resource.

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