K_3,3-free intersection graphs of finite groups

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≠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:

• Finite groups
• intersection graph
• subgroup

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 20D99
• Secondary: 20D15
• 20D25
• 05C25

Acknowledgments

I would like to thank the anonymous referee for the meticulous reading and the shorter arguments he/she provided which greatly enhanced the exposition. This work is completed while I was a visitor in Graz University of Technology. By this occasion, I would like to thank Math C Department of TUGraz for their hospitality.