Laplacian Polynomial

The Laplacian polynomial is the characteristic polynomial of the Laplacian matrix.

The second smallest root of the Laplacian polynomial of a graph g (counting multiple values separately) is known as its algebraic connectivity of g, which the largestis known as the Laplacian spectral radius.

See also

Algebraic Connectivity, Characteristic Polynomial, Laplacian Matrix, Laplacian Spectral Radius

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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, pp. 94-98, 2000.Lin, Z.; Wang, J.; and Cai, M. "The Laplacian Spectral Ratio of Connected Graphs." 21 Feb 2023.

Referenced on Wolfram|Alpha

Laplacian Polynomial

Cite this as:

Weisstein, Eric W. "Laplacian Polynomial." From MathWorld--A Wolfram Web Resource.

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