Are 2 connected graphs isomorphic if they have the same number of vertices and each vertex has the same degree $k$? I don't know how to prove it but I also can't find a counter example.
[Math] Graph isomorphism when all vertices have the same degree
graph theorygraph-isomorphism
Related Question
- [Math] Isomorphic Graph Proof (Degrees of Vertices)
- [Math] Prove that any simple graph with more than one vertex has at least two vertices with the same degree
- [Math] All 2-regular graphs with the same number of vertices are isomorphic to each other.
- [Math] Sufficient condition for graph isomorphism assuming same degree sequence
- Graph Isomorphic: does vertice have to match its corresponding degree
Best Answer
One of them has a three cycle. They are both cubic graphs.