Spectral Characterization of Graphs with Small Second Largest Laplacian Eigenvalue
نویسندگان
چکیده
The family G of connected graphs with second largest Laplacian eigenvalue at most θ, where θ = 3.2470 is the largest root of the equation μ−5μ+6μ−1 = 0, is characterized by Wu, Yu and Shu [Y.R. Wu, G.L. Yu and J.L. Shu, Graphs with small second largest Laplacian eigenvalue, European J. Combin. 36 (2014) 190–197]. Let G(a, b, c, d) be a graph with order n = 2a + b + 2c + 3d + 1 that consists of a triangle(s), b pendant edge(s), c pendant path(s) of length 2 and d pendant path(s) of length 3, sharing a common vertex. In this paper, we first prove that the graph G(a, b, c, d) is determined by its Laplacian spectrum. Then we conclude that except for two graphs, all the graphs in G are determined by their Laplacian spectra.
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تاریخ انتشار 2016