Generalized wreath products of graphs and groups

TL;DR

This paper introduces a new generalized wreath product construction for graphs, extending classical graph products, and proves its relation to Cayley graphs of generalized wreath product groups.

Contribution

It defines the generalized wreath product of graphs and establishes its connection to Cayley graphs of the corresponding group products, unifying existing graph product concepts.

Findings

Generalized wreath product encompasses Cartesian and wreath products as special cases.

Proves the Cayley graph of the generalized wreath product of groups equals the generalized wreath product of Cayley graphs.

Provides a new framework linking graph products with group theory.

Abstract

Inspired by the definition of generalized wreath product of permutation groups, we define the generalized wreath product of graphs, containing the classical Cartesian and wreath product of graphs as particular cases. We prove that the generalized wreath product of Cayley graphs of finite groups is the Cayley graph of the generalized wreath product of the corresponding groups.