a). Given that a directed graph has 17 edges, and 5 vertices, and the following indegrees of the vertices: indegree(a)=5, indegree(b)%36, indegree(c)=3, indegree(d)=1, indegree(e)= X What is the indegree of vertex e? explain why? b). Let G be undirected graph (tree). If you know that the tree G has 25 edges, how many vertices the tree has? Explain why?

Q: (a) Assume there is an adjacency matrix A of an undirected graph G. Further assume a 1 is indicated…

A: - We need to talk about matrix and adjacency list representation for the graph mentioned.

Q: you think finding the "longest path" from p to q can be solved in polynomial time? Given

A: You can solve this using  DFS or applying BFS twice

Q: (a) Recall that the path graph on n vertices has vertex set V = {1,.., n} and edge set E = {{i,i+1}…

A: According to the information given:- We have to recall that path graph on n vertices has vertex set…

Q: Show that the property of being connected is an equivalence relation. That is, for any undirected…

A: Actually, The given information is: That is, for any undirected graph and any two vertices,v, and w,…

Q: 0. A grap onnected

A: For each round of the Bellman ford algorithm, the 'E' edges are relaxed. It takes the same amount of…

Q: = Let G (V, E) be a directed graph. Suppose we have performed a DFS traversal of G, and for each…

A: Proofs for a, b is given below :

Q: 1. Let F be a forest with n vertices and k connected components, with 1 < k <n. (a) Compute ) deg(v)…

A: Answer:  I have given answer in the handwritten format.

Q: 2. Let G = (V, E) be a directed weighted graph with the vertices         V = {A, B, C, D, E, F) and…

A: Computer graphics is the field of computer science and technology that involves creating,…

Q: 1. Given the following un-directed, weighted graph G= {V, E}, where V={ a, b, c, d, e, f), E is the…

A: The adjacenecy matrix representation for the above problem would be: a b c d e fa 0 2 0 0 5 0b 2 0 8…

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: 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: 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: 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: Using C++ programming language solve the following problem: You are given NN points in…

A: please see the next step for solution

Q: Consider the following undirected graph. b s (a) How many edges are there in this graph? (b) Give…

A: (a) The given graph contains the following edges: a self-loop on vertex a (a-b) (a-e) (b-c) (b-d)…

Q: Question 4 Given a undirected weighted graph G = (E,V). With each spanning tree we associate a…

A: First of all we take the labelled edges of spanning trees, which is the maximum age of the spanning…

Q: Consider an undirected graph G with 100 nodes. The maximum number of edges to be included in G so…

A: We are given an undirected graph with 100 nodes and we are asked the maximum number of edges in a…

Q: Problem 6: Let G be a graph with k connected components C₁, C2, ..., Ck, where k ≥ 2. Each connected…

A: here is the solution for your problem,  and the clear explanation for the above one

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).