1. The problem involves analyzing two graphs, G and H, each with 10 vertices (nodes) and multiple edges connecting these vertices. 2. For graph G, observe the number of vertices $V=10$ and count the edges $E$ carefully by tracing each connection between nodes. 3. For graph H, similarly, count the vertices $V=10$ and carefully count the edges $E$ including both straight and curved edges. 4. Use Euler's formula for planar graphs: $$V - E + F = 2$$ where $F$ is the number of faces (regions including the outer one). 5. Verify if the graphs are planar by checking if the edges intersect only at vertices or if there are crossings. 6. Summarize the counts: - For G: $V=10$, count $E$ by listing each edge. - For H: $V=10$, count $E$ similarly. 7. Compare the structure and connectivity of G and H based on vertices and edges. Final answer: Both graphs have 10 vertices. The exact number of edges must be counted carefully from the given description or image. Euler's formula can be used to analyze their planarity and face count.