The largest H-eigenvalue and spectral radius of Laplacian tensor of non-odd-bipartite generalized power hypergraphs

Spectral Characterization of Graphs with Small Second Largest Laplacian Eigenvalue

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 ...

Spectral radius of bipartite graphs

Graphs with small second largest Laplacian eigenvalue

Let L(G) be the Laplacian matrix of G. In this paper, we characterize all of the connected graphs with second largest Laplacian eigenvalue no more than l; where l . = 3.2470 is the largest root of the equation μ3 − 5μ2 + 6μ − 1 = 0. Moreover, this result is used to characterize all connected graphs with second largest Laplacian eigenvalue no more than three. © 2013 Elsevier Ltd. All rights rese...

Regular Uniform Hypergraphs, s-Cycles, s-Paths and Their largest Laplacian H-Eigenvalues∗

In this paper, we show that the largest signless Laplacian H-eigenvalue of a connected k-uniform hypergraph G, where k ≥ 3, reaches its upper bound 2∆(G), where ∆(G) is the largest degree of G, if and only if G is regular. Thus the largest Laplacian H-eigenvalue of G, reaches the same upper bound, if and only if G is regular and oddbipartite. We show that an s-cycle G, as a k-uniform hypergraph...

Bipartite graphs with small third Laplacian eigenvalue

In this paper, all connected bipartite graphs are characterized whose third largest Laplacian eigenvalue is less than three. Moreover, the result is used to characterize all connected bipartite graphs with exactly two Laplacian eigenvalues not less than three, and all connected line graphs of bipartite graphs with the third eigenvalue of their adjacency matrices less than one. c © 2003 Elsevier...