15 May
2020
15 May
'20
12:24 p.m.
Dan Asimov <dasimov@earthlink.net> wrote:
Find a connected graph G on a countably infinite set of vertices such that * each vertex has infinite valence * each vertex is non-adjacent to exactly 2 vertices * any isomorphism of a subgraph H_1 to a subgraph H_2 extends to an isomorphism of the entire graph G to itself.
Note: By a "subgraph" here is mean any collection of the vertices and any collection of the edges which together form a connected graph.
If I understand you correctly, I think the graph that links each integer n to every other integer except n-1 and n+1 would be a solution.