Bipartite graph or not with justification

To determine if a graph is bipartite or not, we can follow these steps:

1. Start by assigning one of the two colors, let's say red, to any arbitrary vertex in the graph.

2. Color all the adjacent vertices of the red vertex with the other color, let's say blue.

3. Repeat step 2 for all the remaining uncolored vertices in the graph, making sure to use the opposite color of their adjacent vertices.

4. If at any point we encounter a vertex that has already been colored and its adjacent vertices have the same color, then the graph is not bipartite.

5. If we are able to color all the vertices without violating the bipartite condition, then the graph is bipartite.

By following these steps, we can determine whether a given graph is bipartite or not.