Geodesic
An Edge but not Vertex Transitive Cubic Graph*
Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 533-535

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Let G be an undirected graph, without loops or multiple edges. An automorphism of G is a permutation of the vertices of G that preserves adjacency. G is vertex transitive if, given any two vertices of G, there is an automorphism of the graph that maps one to the other. Similarly, G is edge transitive if for any two edges (a, b) and (c, d) of G there exists an automorphism f of G such that {c, d} = {f(a), f(b)}. A graph is regular of degree d if each vertex belongs to exactly d edges. 
Bouwer, I. Z. An Edge but not Vertex Transitive Cubic Graph*. Canadian mathematical bulletin, Tome 11 (1968) no. 4, pp. 533-535. doi: 10.4153/CMB-1968-063-0
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     title = {An {Edge} but not {Vertex} {Transitive} {Cubic} {Graph*}},
     journal = {Canadian mathematical bulletin},
     pages = {533--535},
     year = {1968},
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     doi = {10.4153/CMB-1968-063-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-063-0/}
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