Graph Isomorphism by Conversion to Chordal (6, 3) Graphs

TL;DR

This paper presents a reversible transformation method to convert any graph into a chordal (6, 3) graph, enabling the use of automorphism partitions for graph isomorphism testing.

Contribution

It introduces a new reversible transformation technique that converts arbitrary graphs into chordal (6, 3) graphs by using Booth's reduction and eliminating forbidden subgraphs.

Findings

Transformation is reversible and preserves graph automorphisms

Enables automorphism-based graph isomorphism testing for all graphs

Uses Booth's reduction and forbidden subgraph elimination

Abstract

Babel has shown that for an extended class of chordal (6, 3) graphs the coarsest regular simplicial partition is equivalent to the graph's automorphism partition. We give a reversible transformation for any graph to one of these graph by using Booth's reduction of a graph to a chordal graph and elimination of Babel's forbidden subgraphs for these graphs by adding edges to them.