Question: Determine whether the graphs are isomorphic by comparing the number of vertices and edges, and the degrees and connections of vertices. Justify your conclusion using mathematical reasoning. Show all working. Graph 1 is in the lower-left area: vertices $E$, $A$, $C$, $B$, $D$ with edges $E$-$A$, $E$-$C$, $E$-$B$, $B$-$C$, and $B$-$D$. Graph 2 is in the lower-right area: vertices $A$, $E$, $C$, $B$, $D$ with edges $A$-$E$, $E$-$C$, $E$-$B$, $C$-$B$, and $B$-$D$.

1. **State the problem:** Determine if Graph 1 and Graph 2 are isomorphic by comparing vertices, edges, degrees, and connections. 2. **List vertices and edges:** - Graph 1 vertices: $E, A, C, B, D$ - Graph 1 edges: $E$-$A$, $E$-$C$, $E$-$B$, $B$-$C$, $B$-$D$ - Graph 2 vertices: $A, E, C, B, D$ - Graph 2 edges: $A$-$E$, $E$-$C$, $E$-$B$, $C$-$B$, $B$-$D$ 3. **Count vertices and edges:** - Both graphs have $5$ vertices. - Both graphs have $5$ edges. 4. **Calculate degrees of each vertex:** - Graph 1 degrees: - $deg(E) = 3$ (connected to $A, C, B$) - $deg(A) = 1$ (connected to $E$) - $deg(C) = 2$ (connected to $E, B$) - $deg(B) = 3$ (connected to $E, C, D$) - $deg(D) = 1$ (connected to $B$) - Graph 2 degrees: - $deg(E) = 3$ (connected to $A, C, B$) - $deg(A) = 1$ (connected to $E$) - $deg(C) = 2$ (connected to $E, B$) - $deg(B) = 3$ (connected to $E, C, D$) - $deg(D) = 1$ (connected to $B$) 5. **Compare connections:** - Both graphs have the same edges connecting the same vertices. 6. **Conclusion:** - Since both graphs have the same number of vertices and edges, identical degree sequences, and identical connections, they are isomorphic. **Final answer:** Graph 1 and Graph 2 are isomorphic.