Consider the Graph shown below : This graph is a __________.

Answer: Hamiltonian Graph

Explanation:

• What Hamiltonian means: A Hamiltonian graph contains a cycle that visits every vertex exactly once.

• Example Hamiltonian cycle: A → F → B → C → E → D → A. Each consecutive pair in this sequence corresponds to an edge shown in the figure, so this is a valid 6-vertex cycle that visits every vertex once.

• Why the graph is not complete: A complete graph on six vertices would have every vertex connected to all five others. The drawing lacks many of those edges (for example, some corner vertices are not directly joined to certain internal vertices), so it is not complete.

• Why the graph is not bipartite: A bipartite graph cannot contain odd-length cycles. The figure contains a triangle (a 3-cycle) formed by the two top corner vertices and the top internal vertex, which is an odd cycle; therefore the graph is not bipartite.