Spectral radius and extremal graphs for class of unicyclic graph with pendant vertices

The spectral radius of unicyclic and bicyclic graphs with n vertices and k pendant vertices

In this paper, we determine graphs with the largest spectral radius among all the unicyclic and all the bicyclic graphs with n vertices and k pendant vertices, respectively. © 2005 Elsevier Inc. All rights reserved. AMS classification: 05C50

Extremal unicyclic graphs with minimal distance spectral radius

The distance spectral radius ρ(G) of a graph G is the largest eigenvalue of the distance matrix D(G). Let U (n,m) be the class of unicyclic graphs of order n with given matching number m (m 6= 3). In this paper, we determine the extremal unicyclic graph which has minimal distance spectral radius in U (n,m) \ Cn.

The Laplacian Spectral Radius of a Class of Unicyclic Graphs

Let C(n, k) be the set of all unicyclic graphs with n vertices and cycle length k. For anyU ∈ C(n, k),U consists of the (unique) cycle (say Ck) of length k and a certain number of trees attached to the vertices of Ck having (in total) n − k edges. If there are at most two trees attached to the vertices of Ck, where k is even, we identify in the class of unicyclic graphs those graphs whose Lapla...

The Signless Laplacian Spectral Radius for Bicyclic Graphs with k Pendant Vertices

In this paper, we study the signless Laplacian spectral radius of bicyclic graphs with given number of pendant vertices and characterize the extremal graphs.

Order unicyclic mixed graphs by spectral radius