Graph isomorphism testing boosted by path coloring

TL;DR

This paper introduces a novel graph isomorphism testing method that leverages path coloring and tree unrolling to improve discrimination of regular graphs and reduce computational complexity.

Contribution

It presents a new approach combining path coloring and tree unrolling to enhance graph isomorphism testing beyond existing color refinement algorithms.

Findings

Improved discrimination of regular graphs.

Reduced computational complexity in isomorphism testing.

Enhanced vertex partitioning accuracy.

Abstract

A method for improving the efficiency of graph isomorphism testing is presented. The method uses the structure of the graph colored by vertex hash codes as a means of partitioning vertices into equivalence classes, which in turn reduces the combinatorial burden of isomorphism testing. Unrolling the graph into a tree at each vertex allows structurally different regular graphs to be discriminated, a capability that the color refinement algorithm cannot do.