| Title:
|
On the diameter of the intersection graph of a finite simple group (English) |
| Author:
|
Ma, Xuanlong |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
2 |
| Year:
|
2016 |
| Pages:
|
365-370 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
intersection graph |
| Keyword:
|
finite simple group |
| Keyword:
|
diameter |
| MSC:
|
05C25 |
| MSC:
|
20E32 |
| idZBL:
|
Zbl 06604472 |
| idMR:
|
MR3519607 |
| DOI:
|
10.1007/s10587-016-0261-2 |
| . |
| Date available:
|
2016-06-16T12:44:02Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145729 |
| . |
| Reference:
|
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| . |
