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No - consider the vertex-and-edge graph of a truncated cubetruncated cube. Some but not all edges are part of 3-cycles, so this graph is not edge-transitive, but it is clearly edge-swapping.
No - consider the vertex-and-edge graph of a truncated cube. Some but not all edges are part of 3-cycles, so this graph is not edge-transitive, but it is clearly edge-swapping.
No - consider the vertex-and-edge graph of a truncated cube. Some but not all edges are part of 3-cycles, so this graph is not edge-transitive, but it is clearly edge-swapping.
No - consider the vertex-and-edge graph of a truncated cube. Some but not all edges are part of 3-cycles, so this graph is not edge-transitive, but it is clearly edge-swapping.
