ScholarLens Back to search
2023•Unpublished venueOpen access

When is Cartesian product a Cayley graph?

Edward Dobson, Ademir Hujdurović, Wilfried Imrich, Ronald Ortner

Open full text 0 citations

Abstract

A graph is said to be {\it Cayley} graph if its automorphism group admits a regular subgroup. Automorphisms of the Cartesian product of graphs are well understood, and it is known that Cartesian product of Cayley graphs is a Cayley graph. It is natural to ask the reverse question, namely whether all the factors of Cartesian product that is a Cayley graph have to be Cayley graphs. The main purpose of this paper is to initiate the study of this question.

Open-access reader

About this research paper

What this paper is about

A graph is said to be {\it Cayley} graph if its automorphism group admits a regular subgroup. Automorphisms of the Cartesian product of graphs are well understood, and it is known that Cartesian product of Cayley graphs is a Cayley graph. It is natural to ask the reverse question, namely whether all the factors of Cartesian product that is a Cayley graph have to be Cayley graphs. The main purpose of this paper is to initiate the study of this question.

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

A graph is said to be {\it Cayley} graph if its automorphism group admits a regular subgroup. Automorphisms of the Cartesian product of graphs are well understood, and it is known that Cartesian product of Cayley graphs is a Cayley graph. It is natural to ask the reverse question, namely whether all the factors of Cartesian product that is a Cayley graph have to be Cayley graphs. The main purpose of this paper is to initiate the study of this question.

Key concepts: Cayley graph, Cartesian product, Vertex-transitive graph, Cayley's theorem, Automorphism, Cayley transform, Mathematics, Combinatorics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
When is Cartesian product a Cayley graph? — Research Paper | ScholarLens