The Separated Box Product of Two Digraphs
Primo\v{z} Poto\v{c}nik, Stephen Wilson
TL;DR
This paper introduces the separated box product, a novel graph and digraph construction based on the standard box product, exploring its properties, symmetries, and applications to tetravalent edge-transitive graphs.
Contribution
It presents the separated box product construction, analyzes its symmetry properties, and applies it to tetravalent edge-transitive graphs, advancing graph product theory.
Findings
The separated box product has specific symmetry properties.
It relates symmetries of the product to those of the factors.
Application to tetravalent edge-transitive graphs demonstrates its utility.
Abstract
A new product construction of graphs and digraphs, based on the standard box product of graphs and called the separated box product, is presented, and several of its properties are discussed. Questions about the symmetries of the product and their relations to symmetries of the factor graphs are considered. An application of this construction to the case of tetravalent edge-transitive graphs is discussed in detail.
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