“School of Mathematics”
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| Paper IPM / M / 9554 |
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| Abstract: | |||||
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Let k be a natural number and let G be a graph with at least
k vertices. A.E. Brouwer conjectured that the sum of the k largest
Laplacian eigenvalues of G is at most e(G)+((k+1) || 2), where
e(G) is the number of edges of G. We prove this conjecture for
k=2. We also show that if G is a tree, then the sum of the k
largest Laplacian eigenvalues of G is at most e(G)+2k−1.
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