Tricyclic graphs with exactly two main eigenvalues

Xiaoxia Fan; Yanfeng Luo; Xing Gao

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The (signless) Laplacian spectral radius of unicyclic and bicyclic graphs with $n$ vertices and $k$ pendant vertices

Muhuo Liu, Xuezhong Tan, Bo Lian Liu (2010)

Czechoslovak Mathematical Journal

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In this paper, the effects on the signless Laplacian spectral radius of a graph are studied when some operations, such as edge moving, edge subdividing, are applied to the graph. Moreover, the largest signless Laplacian spectral radius among the all unicyclic graphs with $n$ vertices and $k$ pendant vertices is identified. Furthermore, we determine the graphs with the largest Laplacian spectral radii among the all unicyclic graphs and bicyclic graphs with $n$ vertices and $k$ pendant vertices,...