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• W2035584557 abstract "Let G be a graph. The Laplacian matrix, $L( G )$, is $D( G ) - A( G )$, where $D( G )$ is the diagonal matrix of vertex degrees and $A( G )$ is the adjacency matrix. The second immanant of an n-by-n matrix $A = ( a_{ij} )$ is [ d_2 ( A ) = sum_{sigma in S_n } chi ( sigma ) prod_{t = 1}^n a_{tsigma ( t )}, ] where $chi $ is the irreducible character of $S_n $ corresponding to the partition $( 2,1, cdots ,1 )$. The paper concerns various algebraic and combinatorial aspects of the coefficients $c_k ( G )$ in the “$d_2 $-polynomial” [ d_2 ( xI - L ( G ) ) = sum_{k = 0}^n ( - 1 )^k c_k ( G )x^{n - k} . ] For example, the effort to better understand $c_{n - 1} ( G )$ leads to a new definition of “centroid point”. One appendix lists the $d_2 $-polynomials for all graphs on six vertices while a second gives a BASIC program to compute the $d_2$-polynomial." @default.
• W2035584557 created "2016-06-24" @default.
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• W2035584557 date "1986-07-01" @default.
• W2035584557 modified "2023-10-16" @default.
• W2035584557 title "The Second Immanantal Polynomial and the Centroid of a Graph" @default.
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• W2035584557 doi "https://doi.org/10.1137/0607056" @default.
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