Displaying similar documents to “Extremal Unicyclic Graphs With Minimal Distance Spectral Radius”

The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number

Li Su, Hong-Hai Li, Jing Zhang (2014)

Discussiones Mathematicae Graph Theory

Similarity:

In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph PKn−ω,ω among all connected graphs with n vertices and clique number ω. In addition, we show that the spectral radius μ of PKm,ω (m ≥ 1) satisfies [...] More precisely, for m > 1, μ satisfies the equation [...] where [...] and [...] . At last the spectral radius μ(PK∞,ω) of the infinite graph PK∞,ω is also discussed.

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,...

The Laplacian spectral radius of graphs

Jianxi Li, Wai Chee Shiu, An Chang (2010)

Czechoslovak Mathematical Journal

Similarity:

The Laplacian spectral radius of a graph is the largest eigenvalue of the associated Laplacian matrix. In this paper, we improve Shi's upper bound for the Laplacian spectral radius of irregular graphs and present some new bounds for the Laplacian spectral radius of some classes of graphs.

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.