# Integral graphs obtained by dual Seidel switching

## TL;DR

This paper explores how dual Seidel switching can generate new integral graphs, specifically infinite families, by applying the operation to Star and Odd graphs, resulting in new 4-regular integral graphs with known spectra.

## Contribution

The paper introduces two new infinite families of integral graphs obtained via dual Seidel switching, including three new 4-regular integral graphs with explicit spectra.

## Key findings

- Generated new infinite families of integral graphs.
- Identified three new 4-regular integral graphs.
- Spectra of the new graphs are explicitly determined.

## Abstract

Dual Seidel switching is a graph operation introduced by W.~Haemers in 1984. This operation can change the graph, however it does not change its bipartite double, and because of this, the operation leaves the squares of the eigenvalues invariant. Thus, if a graph is integral then it is still integral after dual Seidel switching. In this paper two new infinite families of integral graphs are obtained by applying dual Seidel switching to the Star graphs and the Odd graphs. In particular, three new $4$-regular integral graphs with their spectra are found.