Use graph theory: Let G be a directly acyclic graph with at least two vertices. Suppose we add a directed edge from each sink in G to each source in G. Let the resulting directed graph be called G′. Show that G′ is strongly connected

Q: How many edges does a graph have if its degree sequence is 2, 4, 4, 5, 3? A. Draw a graph with the…

A: Let's solve step by step:

Q: Answer True or False to the following claims: a. Let G be a connected graph on 42 vertices and G…

A: Given questions are true or false questions so we provide both true and false explanation.

Q: Draw the graph G = (V, E) with a vertex-set V = {1,2,3,4}and edge-set E =…

A: Given :- Draw the graph G = (V, E) with a vertex-set V = {1,2,3,4}and edge-set E =…

Q: Compute the vertex set V and edge set E of the graph G=(V,E) whose Prufer Code is (1,2,3,4,5,5)…

A: Vertices in the graph would be equal to the number of terms in prufer code +2.

Q: Suppose that G is an unconnected graph that consists of 4 connected components. The first component…

A: Here i am explaining you , which graph is euler graph:…

Q: Given the following undirected unweighted graph G(V, E). a C What is E? b d e

A: The given graph is G ( V , E ) where , V represent the set of all vertices which is present in a…

Q: A network is considered to be biconnected if every pair of its vertices is linked by two distinct…

A: To demonstrate a biconnected graph without articulation points, let's consider the following graph:…

Q: 1. Draw an undirected graph using the following set of edges.…

A: Undirected graph:- If the edges of the graph are set of unordered pairs of the vertices is called a…

Q: A set of vertices in a graph G = (V,E) is independent if no two of them are adjacent. Let G = (V,E)…

A: The answer is given below:-

Q: Suppose that d 1, d2, ... , dn is a degree sequence. Show that there is a simple graph with vertices…

A: Answer :

Q: Draw a graph with four vertices of degrees 1, 2, 2, and 7 or else explain why no such graph exists.

A: It states that the sum of degrees of the vertices of a graph is equal to twice the number of edges.…

Q: Let G = (V, E) be a graph with vertex-set V = {1, 2, 3, 4, 5} and edge-set E = {(1, 2), (3, 2), (4,…

A: In this question, there are multiple subparts regarding the graph with 5 vertexes {1,2,3,4,5} The…

Q: Let G be a connected planar graph with 32 vertices, 50 edges and degree of each region is k. Find…

A: the value of region as k is calculated in step 2.

Q: 1. Consider the following directed graph. A C F J D G В E H I 1. What are the sources and sinks of…

A: According to the information given:- We have to follow the graph and find the source and sink , one…

Q: Suppose we have a graph G = (V, E) with m edges. Prove that there exists a partition of V into three…

A:

Q: Problem 10: Consider a graph G with 7 vertices whose degrees are 6, 6, 5, 4, 3, 3, 3. (a) Show that…

A: The solution below mention details in step 2

Q: a d b a) Give the vertex set of the G. b) Give the set of edge of G. c) Find the degree of each of…

A: In this question we have been given with the graph and we have to answer for the graph theory…

Q: Consider the following graph: d The directed graph has an Euler circuit. False The directed graph…

A: 1. The directed graph has an Euler circuit. Answer : True An Eulerian cycle exists in a directed…

Q: Question 1 (15 points) a t S a. Find an Euler circuit for the graph above. b. If the edge {a-b} is…

A: Euler circuit for the given graph.

Q: G be a connected graph in which only one node have degree > '1' and rest of nodes are of degree '1'.…

A:

Q: 4. Run the Bellman-Ford algorithm on the directed graph given blow, using vertex z as the source. In…

A: please see the next steps for solutions.

Q: E F B ប A Determine whether the graph contains an Euler path or an Euler circuit. Select the one…

A: Answer: We need to write the given graph is Euler path or Euler circuit. So we will see in the more…

Q: 1. This question is about type of graphs. Construct a graph with exactly 5 nodes such that the graph…

A: We have to construct graphs with exactly 5 nodes such that graph is not connected and graph is not…

Q: Problem 8: Let G be a connected planar graph with n vertices and f faces. Prove that f≤ 2n-4.

A: Answer to the given question

Q: Let G be a graph with distinct vertices u and v. Assume that u and v have degree three and all other…

A: Let G be a graph with distinct vertices  u and  v such that deg ( u ) = deg ( v ) = 3…

Q: Suppose that G is an unconnected graph that consists of 4 connected components. The first component…

A: Euler Graph: A linked graph created by Euler. If there is a closed trail that contains every edge of…

Q: 3. For the graph G= (V, E), find V, Ene all parallel edges, all loops and all isolated verfices and…

A: Solution 1: no given any self loop.

Q: e b d

A: Solution - In the given question, we have to give the outdegree of each vertex.

Q: Draw a simple undirected graph G that has15 vertices, 15 edges.

A: Given:  vertices=15 edges=15

Q: Consider a directed graph G = (V, E), and two distinct vertices u, v E V. Recall that a set of U-V…

A: INTRODUCTION: A directed graph (or digraph) is a graph in mathematics, more especially in graph…

Q: Given the following undirected unweighted graph G(V, E). a C What is E? b d e

A: A graph is an ordered pair (V, E), where V is called the vertex set and E is called the edge set. An…

Q: Prove that if v1 and v2 are distinct vertices of a graph G = (V,E) and a path exists in G from v1 to…

A: Since given graph G = (V, E) have v1 and v2  are distinct vertices and a path exists in G from v1 to…

Q: Determine whether the given graphs have a Euler circu one exists. If no Euler circuit exist,…

A: Answer : Euler Circuit : Euler circuit is a path in a graph in which every edge in the graph must be…

Q: Prove that any graph with the degree sequence 2,5, 5, 7, 7, 7, 7, 7, 7 is Hamiltonian.

A: We need to prove that given graph is Hamiltonian. *** As per the guidelines only 1st question is…

Q: Construct a simple graph with vertices A,B,C,D,E,F whose degrees are 3, 1, 1, 2, 3, 2. (For example,…

A: vertices A,B,C,D,E,F whose degrees are 3, 1, 1, 2, 3, 2. 1,2,1 has edge set

Q: 5. Consider the following graph G (a) How many paths of length 5 are there between vertices 1 and 2?…

A: Hey there, I am writing the required solution based on the above given question. Please do find the…

Q: Suppose we have an undirected graph G with 25 vertices such that the largest independent set in G…

A: Explanation: Vertex cover is a set S of vertices of a graph such that each edge of the graph is…

Q: Given two vertices s and t and a path connecting them, use the knowledge that none of the vertices…

A: Let's assume that we have a graph G that doesn't contain any articulation points. We will prove that…

Q: Consider the following directed graph. b: C: d: a Give the indegree of each vertex. e: e b d

A: In-degree of vertex ->  Numbers of edges coming to vertex is called indegree of that vertex.…

Strongly Connected Components

 A directed graph in which a path exists between all its pairs of vertices is called a strongly connected graph. A portion of the strongly connected directed graph that contains a path to reach from each vertex to other vertices is called a strongly connected component (SCC).