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A non-plain virtually free group with a strictly 2-geodetic Cayley graph
We construct an explicit infinite virtually free group $G=C_4\ast_{C_2}D_3$ with a finite inverse-closed generating set whose Cayley graph is $2$-geodetic but not geodetic. More precisely, we describe the full language of geodesics and show that every element of $G$ has a unique geodesic representat
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