Question 9 3 pts What is the maximum possible number of edges in a directed graph...
Let G be a directed graph on n vertices and maximum possible directed edges; assume that n ≥ 2. (a) How many directed edges are in G? Present such a digraph when n = 3 assuming vertices are 1, 2, and 3. You do not have to present a diagram, if you do not want to; you can simply present the directed edges as a set of ordered pairs. b) Is G, as specified in the problem, reflexive? Justify briefly....
What is the maximum possible number of edges in a graph with n vertices if: (a) the graph is simple? (b) the graph is acyclic? (c) the graph is planar? Try to justify your answers. [Hint: first look at graphs with few vertices.] Need a clear answer with good neat handwriting please.
5. The in-degree of a vertex in a directed graph is the number of edges directed into it. Here is an algorithm for labeling each vertex with its in-degree, given an adjacency-list representation of the graph. for each vertex i: i.indegree = 0 for each vertex i: for each neighbor j of i: j.indegree = j.indegree + 1 Label each line with a big-bound on the time spent at the line over the entire run on the graph. Assume that...
What is the maximum number of edges that a graph on 7 vertices can have if it contains no K3(the complete graph on 3 vertices)?
For a directed graph the in-degree of a vertex is the number of edges it has coming in to it, and the out- degree is the number of edges it has coming out. (a) Let G[i,j] be the adjacency matrix representation of a directed graph, write pseudocode (in the same detail as the text book) to compute the in-degree and out-degree of every vertex in the Page 1 of 2 CSC 375 Homework 3 Spring 2020 directed graph. Store results...
8. For each of the following, either draw a undirected graph satisfying the given criteria or explain why it cannot be done. Your graphs should be simple, i.e. not having any multiple edges (more than one edge between the same pair of vertices) or self-loops (edges with both ends at the same vertex). [10 points] a. A graph with 3 connected components, 11 vertices, and 10 edges. b. A graph with 4 connected components, 10 vertices, and 30 edges. c....
Draw a planar graph(with no loops or multiple edges) for each of the following properties, if possible. If not possible, explain briefly why not. b) 8 vertices, all of degree 3 ( how many edges and regions must there be) c) has exactly 7 vertices, has an euler cycle and 3 is minimum vertex coloring number Also please draw the graph.
2. What is the maximal possible number of edges in an undirected graph with n vertices. Explain your answer briefly.
4. Given a commected weighted directed graph with n vertices, what is the maximum mumber of possible tours in the Traveling Salesman Problem? 5. In the n-Queens problem as given in the textbook, where it is assumed that no two queens can occupy the same row on annx n chessboard, how many nodes are there in the total stat space tree without pruning? 6. As in the previous question, how many leaf nodes in the state space tree? z2 7....
Remarks: All the graphs here are without self loops and parallel edges, and anti-parallel edges. When we speak of a flow network, we mean there are capacities c(e) ? 0 on the edges, the graph G is directed with a source s and a destination t. In all the algorithms, always explain their correctness and analyze their complexity. The complexity should be as small as possible. A correct algorithm with large complexity, may not get full credit. • Question 3:...