Geodesic
Every finite group has a normal bi-Cayley graph
Ars Mathematica Contemporanea, Tome 14 (2018) no. 1, pp. 177-186.

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A graph Γ with a group H of automorphisms acting semiregularly on the vertices with two orbits is called a bi-Cayley graph over H. When H is a normal subgroup of Aut(Γ), we say that Γ is normal with respect to H. In this paper, we show that every finite group has a connected normal bi-Cayley graph. This improves a theorem by Arezoomand and Taeri and provides a positive answer to a question reported in the literature.
DOI : 10.26493/1855-3974.1298.937
Keywords: Normal, bi-Cayley, Cartesian product. 
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Jin-Xin Zhou. Every finite group has a normal bi-Cayley graph. Ars Mathematica Contemporanea, Tome 14 (2018) no. 1, pp. 177-186. doi : 10.26493/1855-3974.1298.937. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1298.937/

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