A Cartesian graph-decomposition theorem based on a vertex-removing synchronised graph product

TL;DR

This paper introduces a new graph-decomposition theorem using a vertex-removing synchronised product, extending Cartesian decomposition techniques for applications in synchronising real-time processes.

Contribution

It presents a novel Cartesian graph-decomposition theorem based on the VRSP, advancing the theoretical framework for graph products related to synchronisation.

Findings

New graph-decomposition theorem established

Extension of Cartesian decomposition techniques

Potential applications in synchronising real-time processes

Abstract

Recently, we have introduced and modified two graph-decomposition theorems based on a new graph product, motivated by applications in the context of synchronising periodic real-time processes. This vertex-removing synchronised product (VRSP), is based on modifications of the well-known Cartesian product and is closely related to the synchronised product due to W\"ohrle and Thomas. Here, we introduce a new graph-decomposition theorem based on the VRSP that provides a Cartesian decomposition of graphs.