Graphs with fourth Laplacian eigenvalue less than two

Authors:
Xiao-Dong Zhang
Affiliations:
Department of Mathematics, Shanghai Jiao Tong University, 1954 Huashan, Shanghai 200030, China
Venue:
European Journal of Combinatorics
Year:
2003

Citing 4
Cited 3

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On the second largest eigenvalue of line graphs

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Nonsingular mixed graphs with few eigenvalues greater than two

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Signless Laplacian eigenvalues and circumference of graphs

Discrete Applied Mathematics
Graphs with small second largest Laplacian eigenvalue

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Abstract

In this paper, all connected graphs with the fourth largest Laplacian eigenvalue less than two are determined, which are used to characterize all connected graphs with exactly three Laplacian eigenvalues no less than two. Moreover, we determine bipartite graphs such that the adjacency matrices of their line graphs have exactly three nonnegative eigenvalues.