The separated box product of two digraphs

Primož Potočnik, Stephen E Wilson

Research output: Contribution to journalArticle

Abstract

A new product construction of graphs and digraphs, called the separated box product, is presented, and several of its properties are discussed. The construction is based on the standard box product of digraphs. However, unlike the standard box product, it preserves the valence of the factor digraphs: If every vertex in both factors has in-valence and out-valence k for some fixed k, then so does every vertex of the separated box product. 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.

Original languageEnglish (US)
Pages (from-to)35-49
Number of pages15
JournalEuropean Journal of Combinatorics
Volume62
DOIs
StatePublished - May 1 2017

Fingerprint

Box Product
Digraph
Edge-transitive Graph
Factor Graph
Symmetry
Vertex of a graph
Graph in graph theory

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

The separated box product of two digraphs. / Potočnik, Primož; Wilson, Stephen E.

In: European Journal of Combinatorics, Vol. 62, 01.05.2017, p. 35-49.

Research output: Contribution to journalArticle

@article{a249bd059b8845e1b3b8d83dea3a6083,
title = "The separated box product of two digraphs",
abstract = "A new product construction of graphs and digraphs, called the separated box product, is presented, and several of its properties are discussed. The construction is based on the standard box product of digraphs. However, unlike the standard box product, it preserves the valence of the factor digraphs: If every vertex in both factors has in-valence and out-valence k for some fixed k, then so does every vertex of the separated box product. 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.",
author = "Primož Potočnik and Wilson, {Stephen E}",
year = "2017",
month = "5",
day = "1",
doi = "10.1016/j.ejc.2016.11.007",
language = "English (US)",
volume = "62",
pages = "35--49",
journal = "European Journal of Combinatorics",
issn = "0195-6698",
publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - The separated box product of two digraphs

AU - Potočnik, Primož

AU - Wilson, Stephen E

PY - 2017/5/1

Y1 - 2017/5/1

N2 - A new product construction of graphs and digraphs, called the separated box product, is presented, and several of its properties are discussed. The construction is based on the standard box product of digraphs. However, unlike the standard box product, it preserves the valence of the factor digraphs: If every vertex in both factors has in-valence and out-valence k for some fixed k, then so does every vertex of the separated box product. 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.

AB - A new product construction of graphs and digraphs, called the separated box product, is presented, and several of its properties are discussed. The construction is based on the standard box product of digraphs. However, unlike the standard box product, it preserves the valence of the factor digraphs: If every vertex in both factors has in-valence and out-valence k for some fixed k, then so does every vertex of the separated box product. 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.

UR - http://www.scopus.com/inward/record.url?scp=85007071606&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85007071606&partnerID=8YFLogxK

U2 - 10.1016/j.ejc.2016.11.007

DO - 10.1016/j.ejc.2016.11.007

M3 - Article

VL - 62

SP - 35

EP - 49

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

SN - 0195-6698

ER -