1. Is each of the graph a simple graph, or a multigraph, or a pseudograph, or a

Question

1. Is each of the graph a simple graph, or a multigraph, or a pseudograph, or a digraph, or a directed multigraph?

2. What is the degree of vertex d in G1?

3. What is the degree of vertex e in G2? What is the in-degree of e in G2? What is the out-degree of e in G2?

4. Using the handshaking theorem, calculate the number of edges in each graph.

5. What is the adjacency matrix for each graph?

6. What is the shortest possible path from the vertex a to vertex d in G1? What is a path from vertex d to vertex a in G2? [Note: you will need to label the edges to specify a path]

7. Does there exist a cycle in graph G1 that covers all its vertices? If so, show the cycle.

8. Does there exist a cycle in graph G2 that covers all its vertices? If so, show the cycle.

9. Is G1 a connected graph?

10. Is G2 a strongly connected graph? Is G2 a weakly connected graph?

11. Does there exist a cut edge in either of the graphs? Argue your answer.

Explanation / Answer

1)Multigraph

2)Degree(d) in G1=4

3) in-degree of e in G2 =3

out-degree of e in G2 = 2

degree(e) in G2 = in-degree+out-degree of e = 3+2 =5

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