Group for Research in Decision Analysis

# Spectral radius of some infinite graphs

## Dragan Stevanovic – University of Nis, Serbia

There are several interesting classes of finite graphs which may be characterized as subgraphs of a certain infinite graph, as is the case with the folklore example of trees with given maximum degree. The spectral radius of the infinite graph is then always an upper bound on the spectral radius of finite graphs from the class. Interestingly, in a number of cases it is much easier to find the spectral radius of the infinite graph than of any of its finite parts ...

We will study here a class of infinite graphs (which, in turn, means a class of classes of finite graphs) and show how to calculate their spectral radius. As an application, we obtain easier proofs for two results bounding the spectral radius of trees and unicyclic graphs with given maximum degree.