On Cubic Nonsymmetric Cayley Graphs - Open Journal of Discrete Mathematics

OJDM > Vol.3 No.1, January 2013

On Cubic Nonsymmetric Cayley Graphs ()

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DOI: 10.4236/ojdm.2013.31008 3,549 Downloads 6,077 Views Citations

Author(s)

Jingjian Li, Bengong Lou, Rui Wang

Affiliation(s)

School of Mathematics and Information Sciences, Guangxi University, Nanning, China.
School of Mathematics and Statistics, Yunnan University, Kunming, China.

ABSTRACT

Let

be a connected Cayley graph of group G, then Γ is called normal if the right regular representation of G is a normal subgroup of , the full automorphism group of Γ. For the case where G is a finite nonabelian simple group and Γ is symmetric cubic Cayley graph, Caiheng Li and Shangjin Xu proved that Γ is normal with only two exceptions. Since then, the normality of nonsymmetric cubic Cayley graph of nonabelian simple group aroused strong interest of people. So far such graphs which have been known are all normal. Then people conjecture that all of such graphs are either normal or the Cayley subset consists of involutions. In this paper we give an negative answer by two counterexamples. As far as we know these are the first examples for the non-normal cubic nonsymmetric Cayley graphs of finite nonabelian simple groups.

KEYWORDS

Cubic Cayley Graph; Nonsymmetric; Non-Normal

Share and Cite:

J. Li, B. Lou and R. Wang, "On Cubic Nonsymmetric Cayley Graphs," Open Journal of Discrete Mathematics, Vol. 3 No. 1, 2013, pp. 39-42. doi: 10.4236/ojdm.2013.31008.

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