The problem asks for the shortest path between nodes $b$ and $z$ in a weighted graph. Let’s analyze the graph and calculate the shortest path.

Given Graph:

1. Nodes and weights are labeled clearly in the graph.
2. We will use Dijkstra's Algorithm to find the shortest path from $b$ to $z$.

Step-by-Step Solution:

1. Initialization:

   • Start at $b$ with distance $0$.
   • All other nodes are initialized with $\infty$ distance.

2. Graph Exploration:

   • From $b$, examine its neighbors:
     • $d$ → Distance $5$ (path $b \to d$).
     • $c$ → Distance $2$ (path $b \to c$).
   • Update distances:
     • $d = 5$, $c = 2$.

3. Move to Node with Smallest Distance:

   • Next, move to $c$ (distance $2$):
     • $c \to e$: Distance $2 + 6 = 8$.
   • Update distance:
     • $e = 8$.

4. Move to $d$ (distance $5$):

   • $d \to f$: Distance $5 + 5 = 10$.
     • $d \to e$: Distance $5 + 1 = 6$ (better than $8$).
   • Update distances:
     • $e = 6$, $f = 10$.

5. Move to $e$ (distance $6$):

   • $e \to g$: Distance $6 + 5 = 11$.
   • Update distance:
     • $g = 11$.

6. Move to $f$ (distance $10$):

   • $f \to z$: Distance $10 + 7 = 17$.
   • Update distance:
     • $z = 17$.

7. Move to $g$ (distance $11$):

   • $g \to z$: Distance $11 + 4 = 15$ (better than $17$).
   • Update distance:
     • $z = 15$.

Shortest Path:

The shortest path from $b$ to $z$ is:

$b \to d \to e \to g \to z$

Total Weight: $5 + 1 + 5 + 4 = 15$.

Correct Answer:

The correct choice is (d): $b, d, e, g, z$.

Let me know if you want me to explain Dijkstra's algorithm in more detail or if you have further questions!

Related Questions:

1. What is Dijkstra's Algorithm, and how does it work?
2. Can you explain why $b \to d \to f \to z$ is not the shortest path?
3. What is the significance of edge weights in shortest path problems?
4. How can we apply this method to a larger graph with more nodes?
5. What are other algorithms to find shortest paths besides Dijkstra?

Tip:

When solving shortest path problems, always ensure you update distances dynamically and check for better paths to nodes you've already visited!