Maximizing Laplacian spectral radius over trees with fixed diameter

Abstract

In this article, we consider the following problem: Of all trees on n vertices with diameter d (both fixed) which tree achieves the maximal Laplacian spectral radius? We show that the maximal Laplacian spectral radius is obtained uniquely at , where is a tree obtained by taking a path P on d + 1 vertices and adding n-d-1 pendant vertices to a center point of P.

Keywords:

• Bipartite graph
• Tree
• Laplacian spectral radius
• Diameter
• Center points
• Subject Classifications:
• O5C5O

Acknowledgement

The authors wish to thank Prof. S. Pati for bringing the problem and a few related references to our attention.