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Superficial edits; added reference for the correct and well-known claim in the first sentence. Meaning and style preserved. Question seems rather vague and difficult and broad, in that 'How' and 'change' are intuitive terms.

edit approved Aug 18, 2017 at 17:36

Peter Heinig

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If L is the laplacian matrix of an undirected graph, and D is a diagonal matrix, what does the cofactor of L+D look like?

We know (e.g. [Godsil, Royle: Algebraic Graph Theory, Lemma 13.2.3]) that any cofactor of the Laplacian matrix of a graph is constant, and is equal to the number of spanning trees of the graph. How do the cofactors change if I just add a diagonal matrix to the Laplacian matrix?

Any help would be greatly appreciated.

asked Jun 27, 2014 at 23:48

user54452