Displaying similar documents to “Tricyclic graphs with exactly two main eigenvalues”

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

Similarity:

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,...

Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth

Kamal Lochan Patra, Binod Kumar Sahoo (2013)

Czechoslovak Mathematical Journal

Similarity:

In this paper we consider the following problem: Over the class of all simple connected unicyclic graphs on n vertices with girth g ( n , g being fixed), which graph minimizes the Laplacian spectral radius? Let U n , g be the lollipop graph obtained by appending a pendent vertex of a path on n - g ( n > g ) vertices to a vertex of a cycle on g ≥ 3 vertices. We prove that the graph U n , g uniquely minimizes the Laplacian spectral radius for n ≥ 2 g - 1 when g is even and for n ≥ 3 g - 1 when g is odd.