If you reverse all the edges of a directed graph, the strongly connected components remain the same. Why is that?

Q: May contain loops and it may contain multiple directed edges that start and end at the same…

A: 1) may conatin loops and it may contain multiple directed edges that start and end at the same…

Q: If the edges in a path are distinct, it is called:a) simple pathb) simple graphc) length of the…

A:

Q: If a graph has 5 edges, how many vertices does it have?

A:

Q: Prove that there must be at least two vertices with the same degree in a simple graph

A:

Q: A square with two diagonals drawn is a complete graph. True False

A:

Q: Determine whether the following graph is bipartite or not. Justify your answer either by giving a…

A:

Q: Show that the maximum number of edges in a graph with n-vertices is *C2 (d)

A:

Q: Show that in a simple graph with at least Two vertices there must be two vertices that have the same…

A:

Q: Consider a complete graph with 6 vertices labeled A, B, F. (a) If you can start at any vertex, how…

A: Step-1 Consider a graph with 6 vertices, For complete graph with n vertices there exist   n-1!2…

Q: If a graph has vertices of degrees 1, 5, 2, 3, and 3, how many edges does it have? Why?

A: We are given a graph that has vertices of degrees 1,5 ,2, 3,3 Now, by Handshaking lemma we have: Sum…

Q: Give an example of a graph with five vertices of degree 1, and six vertices of degree 2. If you…

A:

Q: 1) Determine whether the graph shown has directed or undirected edges, whether it has multiple…

A: Directed graph: A directed graph is a graph in which all the vertices are connected together, where…

Q: . How many nonisomorphic directed simpe graphs are there with 4 vertices?

A: According to the given information, it is required to find number of non-isomorphic directed simple…

Q: d. Add up all the indegrees, and add up all the outdegrees. What do you notice? Can you explain why…

A:

Q: What would be the most appropriate qualification of the following graph? It is a directed…

A: 1. Given graph is We observe that there are multiple arcs with same source and destination in the…

Q: How many vertices will a graphs have if it contains 16 edges and all vertices of degree 2

A: Let G be a graph having 16 edges and all vertices having degree 2

Q: Suppose that we have a graph with at least two vertices. Show that it is not possible that all…

A: Suppose, we have a graph with at least two vertices.

Q: show that a simple planar connected graph with 17 edges and ten vertices cannot be properly colored…

A: We can solve this using Euler theorem

Q: Draw a bipartite graph with a vertex partition into the two sets {v1, v2, v3, v4} and {v5, V6, v7}…

A:

Q: If G1 is a simple graph with 20 edges and G has 25 edges, how many vertices does G1 have?

A:

Q: If a graph has vertices of degrees 1, 1, 2, 3, and 3, how many edges does it have? Why?

A:

Q: Use the pigeonhole principle to prove that a graph has at least two vertices with the same degree

A:

Q: . What is the order and size of the join of two graphs?

A: Given: To explain the given statement is given as,

Q: . Draw a graph with 4 vertices each of degree 2.

A:

Q: Eulerize the following graph using the Edge Walker method:

A:

Q: Draw a directed graph with as few edges as possible that is strongly-connected, has 8 vertices of…

A: Strongly connected directed 8 vertices one has in-degree 3 two have cut degree 3 rest have samller…

Q: Construct the underlying undirected graph for the graphwith directed edges

A: Given: A directed graph G, To sketch: Underlying graph of given graph.

Q: Do the following: 1. Find a graph with 12 edges having six vertices of degree three and the…

A: We need to find a graph with 12 edges, such that 6 vertices have degree three and remaining all the…

Q: There are _____ number of vertices in a graph 6 edges if each vertex is of degree 3.

A:

Q: True or False: The edge set of every closed trail in a graph can be partitioned into edge sets of…

A:

Q: If G is a Hamiltonian graph, then G has no cut-vertex. True or false? Justify

A: In order to find the solution of the given question, we will use the concept of Hamiltonian graph…

Q: 2.29. Is this graph planar (the edges cross each other in the middle but there is no vertex there)?

A: Planar graph: When a connected graph can be drawn without any edges crossing it is called planar.…

Q: ou are working in an organization and it's your primary responsibility to understand the below graph…

A: An edge e is said to be incident on a vertex v if e has one of its endpoints as v. In the given…

Q: Explain why it is not possible to draw a planar graph that contains three faces  and the same number…

A: For any planar graph to exist it should satisfy the Euler formula which is given by - v + f = e + 2…

Q: (a) Is it possible to have a forest with 13 vertices and 10 edges?

A: As per bartleby guidelines i can answer only one question at one time, kindly post rest question…

Q: Label the vertices of the second graph so that it is equivalent to the first graph.

A: Given graphs are,

Q: It is obvious that for a bipartite graph to contain a perfect matching, it is necessary that |A| =…

A: Given That: It is obvious that for a bipartite graph to contain a perfect matching, and also it is…

Q: Consider the following courses and prerequisites: Course | Prereqs 100: 150: 200: 100 250: 150, 200…

A: Given: To find the legal order in which the courses can be taken,

Q: For each course at a university, there may be one or more other courses that are its prerequisites.…

A: According to the provided data, for each course at a university, there may be one or more other…

Q: Consider a complete graph with 6 vertices labeled A, B, ... F. (a) If you can start at any vertex,…

A: Consider the given information.   (a)   First calculate the number of Hamiltonian circuit in 6…

Q: Prove that the sum of the degrees of the vertices of any finite graph is even.

A:

Q: For each of the two directed graphs below,

A: Given, Diagram of two directed graphs and . We have to determined that the given two directed…

Q: The subject is discrete math Part III. Determine the number of vertices and edges and find the…

A:

Q: What is the minimum number of colors you need to color the vertices of this graph such that if two…

A:

Q: By duplicating only 2 edges, Eulerize the following graph:

A:

Q: Give an example of a graph on 8 vertices which is i) Hamiltonian but not Eulerian. ii) Eulerian but…

A: A connected graph G is Hamiltonian if there is a cycle in G which covers every vertex of G exactly…

Q: Are the following directed graphs strongly connected or not? Explain why in detail? 3 4 A

A: A directed graph is said to be strongly connected if there is a path between any pair of vertices in…

Q: The two directed graphs below are isomorphic. Select one: True False

A: