The spectral radius of the square of graphs

TL;DR

This paper investigates bounds on the spectral radius of the square of various classes of graphs, including connected graphs, trees, and unicyclic graphs, with specific focus on properties like girth and diameter.

Contribution

It provides new upper and lower bounds for the spectral radius of the square of these graphs, extending previous spectral graph theory results.

Findings

Established bounds for the spectral radius of squared graphs.

Analyzed spectral radius for unicyclic graphs with fixed girth.

Studied spectral radius of trees with fixed diameter.

Abstract

The square of a connected graph $G$ is obtained from $G$ by adding an edge between every pair of vertices at distance $2$. In this paper we give some upper or lower bounds for the spectral radius of the square of connected graphs, trees and unicyclic graphs respectively.We also investigate the spectral radius of the square of unicyclic graphs with given girth or trees with fixed diameter.