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edit approved Aug 20, 2017 at 3:07
Martin Sleziak
edit approved Aug 20, 2017 at 3:07
Martin Sleziak
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We know (e.g. [Godsil, Royle: Algebraic Graph Theory, Lemma 13.2.3]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.

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.

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.

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.
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edit approved Aug 18, 2017 at 17:36
Peter Heinig
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, what does the cofactor of L+D lookslook 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 treetrees of the graph. How aredo the cofactors change if I just add a diagonal matrix to the Laplacian matrix.?

Any help would be greatly appreciated.

L is the laplacian matrix of an undirected graph, D is a diagonal matrix. What does the cofactor of L+D looks like?

We know that any cofactor of the Laplacian matrix constant, and equal to the number of spanning tree. How are the cofactors change if I just add a diagonal matrix to the Laplacian matrix.

Any help would be greatly appreciated.

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.

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user54452
user54452
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We know that any cofactor of the Laplacian matrix isconstant, and equal to the number of spanning tree; and thus constanttree. The proof that I have seen doesn't seem to tell me howHow are the cofactors would change if I just add a diagonal matrix to the Laplacian matrix.

Any help would be greatly appreciated.

We know that any cofactor of the Laplacian matrix is equal to the number of spanning tree; and thus constant. The proof that I have seen doesn't seem to tell me how the cofactors would change if I just add a diagonal matrix to the Laplacian matrix.

Any help would be greatly appreciated.

We know that any cofactor of the Laplacian matrix constant, and equal to the number of spanning tree. How are the cofactors change if I just add a diagonal matrix to the Laplacian matrix.

Any help would be greatly appreciated.

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user54452
user54452
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