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A conjecture on determining which $(n,k)$-star graphs are not Cayley graphs | | Karimah Sweet
; Li Li
; Eddie Cheng
; László Lipták
; Daniel E. Steffy
; | | Date: |
17 Mar 2017 | | 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 $kgeq 2$ when $n$ is sufficiently
large. For $k=2,dots,15$ we prove that the conjecture is true for all $ngeq
k+2$ (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). | | Source: | arXiv, 1703.6111 | | Services: | Forum | Review | PDF | Favorites | |
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