Understanding Isomorphic Graphs

The video tutorial introduces the concept of isomorphic graphs, explaining that they are essentially the same except for vertex names. It defines isomorphism as a bijection between two graphs that preserves edge connections. An example is provided to determine if two graphs are isomorphic, highlighting the process of building and verifying an isomorphism. The tutorial emphasizes the importance of ensuring the bijection respects edge relations and demonstrates correcting an initial error in the isomorphism attempt.

What is the intuitive idea behind isomorphic graphs?

• They are completely different in structure.

• They have the same number of edges.

• They are identical in structure except for vertex names.

• They have the same number of vertices.

What is a necessary condition for two graphs to be isomorphic?

• They must have the same color.

• They must have the same number of vertices and edges.

• They must have the same vertex labels.

• They must be drawn on the same plane.

What does a bijection ensure in the context of isomorphic graphs?

• Each vertex is mapped to multiple vertices.

• Each vertex is mapped to exactly one vertex.

• Vertices are not mapped at all.

• Vertices are mapped to edges.

In the first attempt to find an isomorphism, what was the issue with the proposed function?

• It was not defined for all vertices.

• It did not respect the edge relations.

• It mapped vertices to the same vertex.

• It was not a bijection.

Why was the first proposed isomorphism not valid?

• It was not defined for any vertex.

• It was not a bijection.

• It did not map all vertices.

• It did not preserve edge connections.

What is the correct mapping for vertex A in G1 to make the graphs isomorphic in the second attempt?

• Vertex A in G2

• Vertex D in G2

• Vertex B in G2

• Vertex C in G2

In the second attempt, which vertex in G1 is mapped to vertex D in G2?

• Vertex A

• Vertex D

• Vertex B

• Vertex C

Which of the following is true about the final isomorphism found?

• It only works for one specific graph.

• It maps all vertices to the same vertex.

• It respects the edge relations.

• It is not a bijection.

What is the significance of edge sets in determining isomorphism?

• They must be identical in both graphs.

• They must be different in both graphs.

• They are irrelevant to isomorphism.

• They must be larger in one graph.

What is the final conclusion about the graphs G1 and G2?

• They are isomorphic.

• They are completely different.

• They are not isomorphic.

• They are identical.