Maximal distance spectral radius of 4-chromatic planar graphs

TL;DR

This paper proves that among all connected 4-chromatic planar graphs with n vertices, the kite graph uniquely has the largest distance spectral radius, highlighting a specific extremal property.

Contribution

The paper establishes the kite graph as the unique maximizer of the distance spectral radius in the class of 4-chromatic planar graphs.

Findings

Kite graph $K_4^{(n)}$ uniquely maximizes the distance spectral radius.

The result applies to all connected 4-chromatic planar graphs.

The paper characterizes extremal properties of the kite graph.

Abstract

We show that the kite graph $K_4^{(n)}$ uniquely maximizes the distance spectral radius among all connected $4$-chromatic planar graphs on $n$ vertices.