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Distance Polynomial


The distance polynomial is the characteristic polynomial of the graph distance matrix.

The following table summarizes distance polynomials for some common classes of graphs.

The following table summarizes the recurrence relations for distance polynomials for some simple classes of graphs.


See also

Characteristic Polynomial, Graph Distance Matrix

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References

Aouchiche, M. and Hansen, P. "Distance Spectra of Graphs: A Survey." Linear Algebra Appl. 458, 301-386, 2014.Balaji, R. and Bapat, R. B. "On Euclidean Distance Matrices." Linear Algebra Appl. 424< 108-117, 2007.Bapat, R. B. Ch. 3 in Graphs and Matrices. New Delhi, India: Springer, 2010.Devillers, J. and Balaban, A. T. (Eds.). Topological Indices and Related Descriptors in QSAR and QSPR. Amsterdam, Netherlands: Gordon and Breach, pp. 96-97, 2000.Ruzieh, S. and Powers, D. L. "The Distance Spectrum of the Path P_n and the First Distance Eigenvector of Connected Graphs." Linear Multilinear Algebra 28, 75-81, 1990.Steinerberger, S. "The First Eigenvector of a Distance Matrix Is Nearly Constant." Disc. Math. 346, 113291, 2023.

Referenced on Wolfram|Alpha

Distance Polynomial

Cite this as:

Weisstein, Eric W. "Distance Polynomial." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DistancePolynomial.html

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