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- W2086540021 abstract "It is shown that if L and D are the Laplacian and the distance matrix of a tree respectively, then any minor of the Laplacian equals the sum of the cofactors of the complementary submatrix of D , up to sign and a power of 2. An analogous, more general result is proved for the Laplacian and the resistance matrix of any graph. A similar identity is proved for graphs in which each block is a complete graph on r vertices, and for q -analogues of such matrices of a tree. Our main tool is an identity for the minors of a matrix and its inverse." @default.
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- W2086540021 date "2011-09-01" @default.
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- W2086540021 title "Identities for minors of the Laplacian, resistance and distance matrices" @default.
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- W2086540021 doi "https://doi.org/10.1016/j.laa.2011.03.028" @default.
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