Given the following directed graph G: a. What is the in-degree of vertex 6? b. What is the out-degree of vertex 4? 3 c. Find a walk of length 5 from vertex 5 to vertex 3. d. Find a path of length 6 from vertex 1 to vertex 2. e. Find a circuit of length 7 starting at vertex 3. 5 f. Find a cycle of length 5 starting at vertex 4. g. Is there an edge from vertex 4 to vertex 5 in G? Why? (6 h. Is there an edge from vertex 4 to vertex 2 in G5? Why?

Q: Analyze each graph and explain why the graph does or does not have an Euler circuit. If it does,…

A: Figure 6 :

Q: 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1 1

A:

Q: 3. Either draw a graph with the specified properties or explain why no such graph exists. a. Graph…

A: Given problem is :

Q: For each graph below, find an Euler circuit in the graph or explain why the graph does not have an…

A: It is known that, “A graph will contain an Euler circuit if all vertices have even degree”.   It is…

Q: D C B E F A Consider the graph given above. Add an edge so the resulting graph has an Euler path…

A: Theorem: A connected graph has an Euler path if and only if it has exactly zero or two vertices of…

Q: Analyze each graph and explain why the graph does or does not have an Euler circuit. If it does,…

A:

Q: 14. Let G be the graph with vertices v1, v2, and v3 as shown below. What is the number of walks of…

A: Walk :- A walk in graph is a sequence of vertices and edges.

Q: Let A and B each be sets of N labeled as vertices, and consider the bipartite between A and B 1.…

A: Given: A, B be any sets of N labeled vertices in each. Bipartite between the set A and B. To find:…

Q: (c) Prove that the two graphs below are isomorphic.

A: Given, We will prove these two graphs are isomorphic.

Q: Determine whether the given graph has an Euler circuit or an Euler path. OA OB OC O a O f d b (A)…

A:

Q: C D B E A Find an Euler path for the graph. Enter your response as a sequence of vertices in the…

A: We have to find an Eulerian path for the given graph.

Q: Consider the following graph G. 4 3 a. Show that G satisfies the general formula that the sum of all…

A:

Q: A cycle in a simple graph is a closed walk of length greater than m. What is the value of m?

A:

Q: How many cycles of length 4 (i.e. 4 edges) are in the complete graph Kg? Note: the cycle 1-2-3-4-1…

A:

Q: Indicate two edges such that after deleting these two edges the resulting graph is bipartite. Then…

A:

Q: b e a f

A: Given: a) b)

Q: best

A: For a Euler Circuit, all vertices must have even degrees. For a Euler path, either 0 or 2 odd degree…

Q: Analyze each graph below to determine whether it has an Euler circuit and/or an Euler trail. •If it…

A: An Euler trail in a graph is defined as a path that visits every edge of the graph exactly once. An…

Q: The Euler's formula v - e + f = 2 holds for all connected planar graphs. What if the graph is not…

A: The formula for multiple connected component c is, v +f = e + c + 1

Q: (iv) Give an example of a closed walk of length four in the graph that is not a circuit. (v) Give…

A: