The Laplacian polynomial is the characteristic
polynomial of the Laplacian matrix .
The second smallest root of the Laplacian polynomial of a graph algebraic
connectivity of 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. 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 https://mathworld.wolfram.com/LaplacianPolynomial.html
Subject classifications
(counting multiple values separately) is known as its algebraic
connectivity of 
, which the largestis known as the Laplacian
spectral radius.
