To determine whether the given pair of graphs $G1$ and $G2$ are isomorphic, we need to examine their structures and match vertices and edges accordingly. Here’s a structured approach:

1. Count the Vertices and Edges:

   • Both graphs should have the same number of vertices and edges if they are to be isomorphic.
   • In $G1$, there are 4 vertices (A, B, C, D) and 6 edges.
   • In $G2$, there are 4 vertices (V1, V2, V3, V4) and 6 edges.

2. Degree of Vertices:

   • Check the degree (number of connections) of each vertex.
   • In $G1$: A, B, C have degree 3, and D has degree 3.
   • In $G2$: V1, V2, V3, and V4 also all have degree 3.

3. Check for Similar Connectivity:

   • Both graphs have the same degree distribution, indicating that a one-to-one mapping might be possible.

4. Circuit Structure:

   • The circuits (closed paths) or cycles should correspond in length.
   • By examining the triangles in $G1$ and corresponding paths in $G2$, we can confirm they have similar structure.

Since all criteria match, the graphs $G1$ and $G2$ are isomorphic.

Would you like a deeper explanation of graph isomorphism? Here are some related questions to explore:

1. What is the significance of degree sequence in graph isomorphism?
2. How can adjacency matrices be used to verify isomorphism?
3. What is a bijective mapping of vertices in the context of isomorphic graphs?
4. Why is preserving the circuit structure important in graph isomorphism?
5. What role do automorphisms play in understanding graph structure?

Tip: When checking graph isomorphism, start by comparing vertex and edge counts, then examine degrees and structural patterns for a quick analysis.