1. The problem involves analyzing two graphs labeled (a) G and (b) H, each with 10 vertices arranged differently and with distinct edge structures. 2. For graph (a) G, the vertices form a roughly rectangular shape with additional edges creating a star inside. This suggests a complex connectivity pattern, possibly a complete bipartite or a star graph overlay. 3. For graph (b) H, the vertices are arranged in a triangular shape with curved edges inside, indicating a different connectivity pattern, possibly involving cycles or chordal edges. 4. To analyze these graphs, we consider properties such as vertex degree, connectivity, cycles, and planarity. 5. Important graph theory rules include: the sum of degrees equals twice the number of edges, Euler's formula for planar graphs ($V - E + F = 2$), and definitions of special graphs like stars, complete graphs, and cycles. 6. Without explicit edge lists or adjacency matrices, we focus on qualitative analysis: G likely has higher connectivity due to the star edges, while H's triangular arrangement suggests fewer edges or a different cycle structure. 7. Final conclusion: G and H are distinct graphs with 10 vertices each, differing in vertex arrangement and edge connectivity, illustrating different graph structures and properties.