New Invariants for the Graph Isomorphism Problem

TL;DR

This paper presents a new polynomial-time algorithm for computing graph invariants using a modified random walk approach, capable of distinguishing certain complex graph instances that previous methods could not resolve.

Contribution

The paper introduces a novel polynomial-time algorithm based on modified random walks, providing new tools for graph isomorphism testing.

Findings

Successfully distinguishes complex graph instances like Furer Gadgets

Provides a new approach to graph invariants with potential for broader application

Not yet proven to be a full graph invariant

Abstract

In this paper we introduce a novel polynomial-time algorithm to compute graph invariants based on the modified random walk idea on graphs. However not proved to be a full graph invariant by now, our method gives the right answer for the graph instances other well-known methods could not compute (such as special Furer Gadgets and point-line incidence graphs of finite projective planes of higher degrees