On a class of maximal reflexive θ-graphs generated by Smith graphs
Marija Rašajski · Applicable Analysis and Discrete Mathematics · 2007
A simple graph is said to be reflexive if its second largest eigenvalue does not exceed 2. The property λ2 ≤ 2 is a hereditary one, i.e. any induced subgraph of a reflexive graph preserves this property and that is why reflexive graphs are usually represented by maximal graphs within a given class. Bicyclic graphs whose two cycles have a common path are called θ-graphs. We consider classes of maximal reflexive θ-graphs arising from a Smith tree and a cycle attached to it in a specified way.