The signless Laplacian spectral radius of bicyclic graphs with prescribed degree sequences

The (Signless Laplacian) Spectral Radii of Connected Graphs with Prescribed Degree Sequences

In this paper, some new properties are presented to the extremal graphs with largest (signless Laplacian) spectral radii in the set of all the connected graphs with prescribed degree sequences, via which we determine all the extremal tricyclic graphs in the class of connected tricyclic graphs with prescribed degree sequences, and we also prove some majorization theorems of tricyclic graphs with...

The signless Laplacian spectral radius of graphs with given degree sequences

The Signless Laplacian or Adjacency Spectral Radius of Bicyclic Graphs with Given Number of Cut Edges

LetB(n, r) be the set of all bicyclic graphs with n vertices and r cut edges. In this paper we determine the unique graph with maximal adjacency spectral radius or signless Laplacian spectral radius among all graphs in B(n, r).

The signless Laplacian spectral radius of bicyclic graphs with a given girth

Let B(n, g) be the class of bicyclic graphs on n vertices with girth g. In this paper, the graphs in B(n, g) with the largest signless Laplacian spectral radius are characterized.

The Signless Laplacian Spectral Radius of Unicyclic and Bicyclic Graphs with a Given Girth

Let U(n, g) and B(n, g) be the set of unicyclic graphs and bicyclic graphs on n vertices with girth g, respectively. Let B1(n, g) be the subclass of B(n, g) consisting of all bicyclic graphs with two edge-disjoint cycles and B2(n, g) = B(n, g)\B1(n, g). This paper determines the unique graph with the maximal signless Laplacian spectral radius among all graphs in U(n, g) and B(n, g), respectivel...