Finite groups whose intersection graphs are planar

Selçuk Kayacan*, Ergün Yaraneri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

The intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if H∩K 6≠ 1 where 1 denotes the trivial subgroup of G. In this paper we characterize all finite groups whose intersection graphs are planar. Our methods are elementary. Among the graphs similar to the intersection graphs, we may count the subgroup lattice and the subgroup graph of a group, each of whose planarity was already considered before in [2, 10, 11, 12].

Original languageEnglish
Pages (from-to)81-96
Number of pages16
JournalJournal of the Korean Mathematical Society
Volume52
Issue number1
DOIs
Publication statusPublished - 2015

Bibliographical note

Publisher Copyright:
© 2015 Korean Mathematical Society.

Keywords

  • Finite groups
  • Intersection graph
  • Planar
  • Subgroup

Fingerprint

Dive into the research topics of 'Finite groups whose intersection graphs are planar'. Together they form a unique fingerprint.

Cite this