On the spectral radius of unicyclic and bicyclic graphs with a fixed diameter

2021/06/17 by Wang, F. F., Shan, H. Y., Zhai, Y. Y.
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.09238

Abstract

The α-spectral radius of a connected graph G is the spectral radius of A_α-matrix of G. In this paper, we discuss the methods for comparing α-spectral radius of graphs. As applications, we characterize the graphs with the maximal α-spectral radius among all unicyclic and bicyclic graphs of order n with diameter d, respectively. Finally, we determine the unique graph with maximal signless Laplacian spectral radius among bicyclic graphs of order n with diameter d.

Related

• On the maximum A_α-spectral radius of unicyclic and bicyclic graphs with fixed girth or fixed number of pendant vertices
• Extremal ABS Spectral Radius in Bicyclic and Bipartite Unicyclic Graphs
• On the α-spectral radius of graphs
• The A_α-spectral radius of graphs with given degree sequence.
• On the maximal α-spectral radius of graphs with given matching number