Linking Rings Structures and tetravalent semisymmetric graphs

Primož Potočnik, Stephen E Wilson

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

In this paper, we introduce LR structures, a new and interesting form of symmetry in graphs. LR structures are motivated by the search for semisymmetric graphs of degree 4. We show that all semisymmetric graphs of girth and degree 4 can be constructed in a simple way from LR structures. We then show several ways in which LR structures can be constructed or found.

Original languageEnglish (US)
Pages (from-to)341-352
Number of pages12
JournalArs Mathematica Contemporanea
Volume7
Issue number2
StatePublished - 2014

Fingerprint

Semisymmetric Graph
Linking
Ring
Girth
Symmetry
Graph in graph theory

Keywords

  • Automorphism group
  • Cycle structure
  • Graph
  • Linking rings structure
  • Locally arc-transitive graph
  • Semisymmetric graph
  • Symmetry

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Algebra and Number Theory
  • Geometry and Topology
  • Theoretical Computer Science

Cite this

Linking Rings Structures and tetravalent semisymmetric graphs. / Potočnik, Primož; Wilson, Stephen E.

In: Ars Mathematica Contemporanea, Vol. 7, No. 2, 2014, p. 341-352.

Research output: Contribution to journalArticle

@article{972042900b9f49b6a9ee4c27db990433,
title = "Linking Rings Structures and tetravalent semisymmetric graphs",
abstract = "In this paper, we introduce LR structures, a new and interesting form of symmetry in graphs. LR structures are motivated by the search for semisymmetric graphs of degree 4. We show that all semisymmetric graphs of girth and degree 4 can be constructed in a simple way from LR structures. We then show several ways in which LR structures can be constructed or found.",
keywords = "Automorphism group, Cycle structure, Graph, Linking rings structure, Locally arc-transitive graph, Semisymmetric graph, Symmetry",
author = "Primož Potočnik and Wilson, {Stephen E}",
year = "2014",
language = "English (US)",
volume = "7",
pages = "341--352",
journal = "Ars Mathematica Contemporanea",
issn = "1855-3966",
publisher = "DMFA Slovenije",
number = "2",

}

TY - JOUR

T1 - Linking Rings Structures and tetravalent semisymmetric graphs

AU - Potočnik, Primož

AU - Wilson, Stephen E

PY - 2014

Y1 - 2014

N2 - In this paper, we introduce LR structures, a new and interesting form of symmetry in graphs. LR structures are motivated by the search for semisymmetric graphs of degree 4. We show that all semisymmetric graphs of girth and degree 4 can be constructed in a simple way from LR structures. We then show several ways in which LR structures can be constructed or found.

AB - In this paper, we introduce LR structures, a new and interesting form of symmetry in graphs. LR structures are motivated by the search for semisymmetric graphs of degree 4. We show that all semisymmetric graphs of girth and degree 4 can be constructed in a simple way from LR structures. We then show several ways in which LR structures can be constructed or found.

KW - Automorphism group

KW - Cycle structure

KW - Graph

KW - Linking rings structure

KW - Locally arc-transitive graph

KW - Semisymmetric graph

KW - Symmetry

UR - http://www.scopus.com/inward/record.url?scp=84892153963&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84892153963&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 341

EP - 352

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

SN - 1855-3966

IS - 2

ER -