An upper bound for higher order eigenvalues of symmetric graphs

TL;DR

This paper establishes an upper bound for higher order eigenvalues of the normalized Laplace operator on symmetric finite graphs, relating them to lower order eigenvalues, which advances spectral graph theory understanding.

Contribution

It introduces a novel upper bound for higher order eigenvalues based on lower order eigenvalues for symmetric graphs.

Findings

Derived an explicit upper bound for higher order eigenvalues.

Connected higher and lower order eigenvalues through this bound.

Enhanced spectral analysis tools for symmetric graphs.

Abstract

In this paper, we derive an upper bound for higher order eigenvalues of the normalized Laplace operator associated with a symmetric finite graph in terms of lower order eigenvalues.