Come up with an example of graphs:
- Graph $G$ without bridges and $G^2$ isn't Hamiltonian Graph.
- Graph $G$ is triconnected graph, local-connected (it means that for all vertices: the environment of a vertex (without itself) is connected graph) and $G$ isn't Hamiltonian Graph
- Graph $G$ is cubic graph, triconnected and $G$ isn't Hamiltonian Graph.
- Graph $G$ is connected, local-Hamiltonian (it means that for all vertices: the environment of a vertex (without itself) is Hamiltonian Graph), and $G$ isn't Hamiltonian Graph.
Why:
- If graph $G$ is connected, local-connected, edge-connected $\Rightarrow$ $G$ is Hamiltonian Graph.
Please give some examples or clues!
Thanks anyway!