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

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

See also Algebraic Connectivity ,

Characteristic Polynomial ,

Laplacian
Matrix ,

Laplacian Spectral Radius
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References 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. https://arxiv.org/abs/2302.10491v1 . Referenced
on Wolfram|Alpha Laplacian Polynomial
Cite this as:
Weisstein, Eric W. "Laplacian Polynomial."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/LaplacianPolynomial.html

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