# On the diameter of the intersection graph of a finite simple group

Czechoslovak Mathematical Journal (2016)

- Volume: 66, Issue: 2, page 365-370
- ISSN: 0011-4642

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topMa, Xuanlong. "On the diameter of the intersection graph of a finite simple group." Czechoslovak Mathematical Journal 66.2 (2016): 365-370. <http://eudml.org/doc/280105>.

@article{Ma2016,

abstract = {Let $G$ be a finite group. The intersection graph $\Delta _G$ of $G$ is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper nontrivial subgroups of $G$, and two distinct vertices $X$ and $Y$ are adjacent if $X\cap Y\ne 1$, where $1$ denotes the trivial subgroup of order $1$. A question was posed by Shen (2010) whether the diameters of intersection graphs of finite non-abelian simple groups have an upper bound. We answer the question and show that the diameters of intersection graphs of finite non-abelian simple groups have an upper bound $28$. In particular, the intersection graph of a finite non-abelian simple group is connected.},

author = {Ma, Xuanlong},

journal = {Czechoslovak Mathematical Journal},

keywords = {intersection graph; finite simple group; diameter},

language = {eng},

number = {2},

pages = {365-370},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On the diameter of the intersection graph of a finite simple group},

url = {http://eudml.org/doc/280105},

volume = {66},

year = {2016},

}

TY - JOUR

AU - Ma, Xuanlong

TI - On the diameter of the intersection graph of a finite simple group

JO - Czechoslovak Mathematical Journal

PY - 2016

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 66

IS - 2

SP - 365

EP - 370

AB - Let $G$ be a finite group. The intersection graph $\Delta _G$ of $G$ is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper nontrivial subgroups of $G$, and two distinct vertices $X$ and $Y$ are adjacent if $X\cap Y\ne 1$, where $1$ denotes the trivial subgroup of order $1$. A question was posed by Shen (2010) whether the diameters of intersection graphs of finite non-abelian simple groups have an upper bound. We answer the question and show that the diameters of intersection graphs of finite non-abelian simple groups have an upper bound $28$. In particular, the intersection graph of a finite non-abelian simple group is connected.

LA - eng

KW - intersection graph; finite simple group; diameter

UR - http://eudml.org/doc/280105

ER -

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