Faster FPT Algorithm for Graph Isomorphism Parameterized by Eigenvalue Multiplicity

TL;DR

This paper presents a faster fixed-parameter tractable algorithm for testing graph isomorphism in graphs with bounded eigenvalue multiplicity, significantly improving the previous time bounds.

Contribution

It introduces an $O^*(k^{O(k)})$ algorithm for graph isomorphism when eigenvalue multiplicity is bounded by $k$, advancing the computational efficiency in this domain.

Findings

Improved the time complexity from $O^*(2^{O(k^2/ ext{log }k)})$ to $O^*(k^{O(k)})$.

Applicable to graphs with eigenvalue multiplicity bounded by $k$.

Demonstrated theoretical advancement in fixed-parameter algorithms for graph isomorphism.

Abstract

We give a $O^*(k^{O(k)})$ time isomorphism testing algorithm for graphs of eigenvalue multiplicity bounded by $k$ which improves on the previous best running time bound of $O^*(2^{O(k^2/\log k)})$.