Note on deleting a vertex and weak interlacing of the Laplacian spectrum
نویسندگان
چکیده
The question of what happens to the eigenvalues of the Laplacian of a graph when we delete a vertex is addressed. It is shown that λi − 1 ≤ λi ≤ λi+1, where λi is the ith smallest eigenvalues of the Laplacian of the original graph and λ v i is the ith smallest eigenvalues of the Laplacian of the graph G[V −v]; i.e., the graph obtained after removing the vertex v. It is shown that the average number of leaves in a random spanning tree F(G) > 2|E|e −1 α λn , if λ2 > αn.
منابع مشابه
Ela Note on Deleting a Vertex and Weak Interlacing of the Laplacian Spectrum∗
The question of what happens to the eigenvalues of the Laplacian of a graph when we delete a vertex is addressed. It is shown that λi − 1 ≤ λi ≤ λi+1, where λi is the ith smallest eigenvalues of the Laplacian of the original graph and λ v i is the ith smallest eigenvalues of the Laplacian of the graph G[V −v]; i.e., the graph obtained after removing the vertex v. It is shown that the average nu...
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