{
"id": "1703.06111",
"version": "v1",
"published": "2017-03-17T17:22:17.000Z",
"updated": "2017-03-17T17:22:17.000Z",
"title": "A conjecture on determining which $(n,k)$-star graphs are not Cayley graphs",
"authors": [
"Karimah Sweet",
"Li Li",
"Eddie Cheng",
"László Lipták",
"Daniel E. Steffy"
],
"categories": [
"math.CO",
"math.GR"
],
"abstract": "In this paper, we continue the work begun by Cheng et al.~on classifying which of the $(n,k)$-star graphs are Cayley. We present a conjecture for the complete classification, and prove an asymptotic version of the conjecture, that is, the conjecture is true for all $k\\geq 2$ when $n$ is sufficiently large. For $k=2,\\dots,15$ we prove that the conjecture is true for all $n\\geq k+2$ (with the possible exception of $S_{17,14}$). The proof reveals some unexpected connection between $(n,k)$-star graphs and the classification of multiply transitive groups (which is closely related to the classification of finite simple groups).",
"revisions": [
{
"version": "v1",
"updated": "2017-03-17T17:22:17.000Z"
}
],
"analyses": {
"subjects": [
"05C25",
"20D05"
],
"keywords": [
"star graphs",
"conjecture",
"cayley graphs",
"finite simple groups",
"work begun"
],
"note": {
"typesetting": "TeX",
"pages": 0,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}