“School of Mathematics”
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| Paper IPM / M / 11365 | ||||||||||||||||||||||
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| Abstract: | ||||||||||||||||||||||
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We investigate graphs whose signless Laplacian matrix has
three distinct eigenvalues. We show that the largest signless
Laplacian eigenvalue of a connected graph G with three distinct
signless Laplacian eigenvalues is noninteger if and only if
G=Kn−e for n ≥ 4, where Kn−e is the n vertex
complete
graph with an edge removed. Moreover, examples of such graphs
are given.
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