Which of the following graph is/are planer? Choose the most appropriate answer…

A graph is planar if it can be drawn on a plane without any edges crossing. We analyze each graph:

• Graph (A): This graph is planar because the given drawing has no edge crossings. It is already in a planar embedding.

• Graph (B): This graph appears to have edge crossings, but it is planar because the vertices can be rearranged to eliminate all crossings. Planarity depends on the existence of a crossing-free drawing, not the given one.

• Graph (C): This graph is non-planar. It contains a subgraph that is homeomorphic to the utility graph (K3,3), which is a known non-planar graph. No matter how the vertices are arranged, at least one edge crossing will occur.

Therefore, only graphs A and B are planar.