Spectral ordering and 2-switch transformations

Abstract

We address the problem of ordering trees with the same degree sequence by their spectral radii. To achieve that, we consider 2-switch transformations which preserve the degree sequence and establish when the index decreases. Our main contribution is to determine a total ordering of a particular family by their indices according to a given parameter related to sizes in the tree.

Keywords

• Spectral radius
• Tree
• 2-switch
• Ordering