1. **Problem:** Find the number of vertices, edges, and degree of each vertex in graph G. 2. **Step 1: Identify vertices and edges in G.** - Vertices: a, b, c, d, e, f - Edges: From description, G has a square formed by vertices a, b, f, e with edges (a-b), (b-f), (f-e), (e-a) plus a diagonal (b-f). Vertex c is isolated. 3. **Step 2: Count vertices and edges.** - Number of vertices $= 6$ - Edges in square: 4 - Diagonal edge: 1 - Total edges $= 5$ 4. **Step 3: Degree of each vertex.** - $\deg(a) = 2$ (edges a-b, a-e) - $\deg(b) = 3$ (edges b-a, b-f, diagonal b-f counted once) - $\deg(c) = 0$ (isolated) - $\deg(d)$ not mentioned, assume 0 or no edges - $\deg(e) = 2$ (edges e-a, e-f) - $\deg(f) = 3$ (edges f-b, f-e, diagonal b-f counted once) 5. **Step 4: Identify isolated and pendant vertices.** - Isolated vertex: c (degree 0) - Pendant vertices: vertices with degree 1, none here 6. **Step 5: Sum of degrees and verify with edges.** - Sum degrees $= 2 + 3 + 0 + 0 + 2 + 3 = 10$ - Twice the number of edges $= 2 \times 5 = 10$ - Verified: sum of degrees equals twice the number of edges. **Final answer:** - Number of vertices: 6 - Number of edges: 5 - Degrees: $\deg(a)=2$, $\deg(b)=3$, $\deg(c)=0$, $\deg(d)=0$, $\deg(e)=2$, $\deg(f)=3$ - Isolated vertex: c - No pendant vertices