Construction of cospectral graphs

TL;DR

This paper introduces a novel graph-theoretic method using partial transpose to construct non-isomorphic cospectral graphs, addressing a complex problem in spectral graph theory especially for large graphs.

Contribution

It proposes the graph theoretical partial transpose as a new tool for generating non-isomorphic cospectral graphs from clustered graphs.

Findings

Partial transpose can produce cospectral graphs

Method applicable to large graphs

Potential for advancing spectral graph theory

Abstract

Construction of non-isomorphic cospectral graphs is a nontrivial problem in spectral graph theory specially for large graphs. In this paper, we establish that graph theoretical partial transpose of a graph is a potential tool to create non-isomorphic cospectral graphs by considering a graph as a clustered graph.