$K_{3,3}$-free Intersection Graphs of Finite Groups

Selçuk Kayacan

$K_{3,3}$-free Intersection Graphs of Finite Groups

Group Theory 2016-08-03 v2 Combinatorics

Authors: Selçuk Kayacan

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 $H\cap K \neq 1$ where $1$ denotes the trivial subgroup of $G$ . In this paper we classify all finite groups whose intersection graphs are $K_{3,3}$ -free.

Keywords

intersection graph finite group subgroup K_{3,3}-free graph graph classification proper non-trivial subgroup group theory

Cite

@article{arxiv.1512.05113,
  title  = {$K_{3,3}$-free Intersection Graphs of Finite Groups},
  author = {Selçuk Kayacan},
  journal= {arXiv preprint arXiv:1512.05113},
  year   = {2016}
}

Comments

Proof of Proposition 10 is due to the anonymous referee

$K_{3,3}$-free Intersection Graphs of Finite Groups

Abstract

Keywords

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