Base graph–connection graph: Dissection and construction

Primož Potočnik, Gabriel Verret, Stephen Wilson

Research output: Contribution to journalArticlepeer-review

Abstract

This paper presents a phenomenon which sometimes occurs in tetravalent bipartite locally dart-transitive graphs, called a Base Graph–Connection Graph dissection. In this dissection, each white vertex is split into two vertices of valence 2 so that the connected components of the result are isomorphic. Given the Base Graph whose subdivision is isomorphic to each component, and the Connection Graph, which describes how the components overlap, we can, in some cases, provide a construction which can make a graph having such a decomposition. This paper investigates the general phenomenon as well as the special cases in which the connection graph has no more than one edge.

Original languageEnglish (US)
Pages (from-to)116-128
Number of pages13
JournalDiscrete Applied Mathematics
Volume291
DOIs
StatePublished - Mar 11 2021

Keywords

  • 4-valent
  • Arc-transitive
  • Edge-transitive
  • Graph
  • Locally dart-transitive
  • Semisymmetric
  • Tetravalent

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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