The spectral radius of subgraphs of regular graphs

TL;DR

This paper establishes bounds on the spectral radius and smallest eigenvalue of subgraphs and nonbipartite regular graphs with specified order and diameter, advancing spectral graph theory understanding.

Contribution

It provides new bounds on spectral properties of subgraphs and nonbipartite regular graphs based on order and diameter parameters.

Findings

Bound on the spectral radius of subgraphs of regular graphs.

Lower bound on the smallest eigenvalue of nonbipartite regular graphs.

Results applicable to graphs with given order and diameter.

Abstract

We give a bound on the spectral radius of subgraphs of regular graphs with given order and diameter. We give a lower bound on the smallest eigenvalue of a nonbipartite regular graph of given order and diameter.