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Discrete Math
Consider the following directed graph. Give the indegree of each vertex.
discrete math a. Consider the following rooted tree: 7 10 11 12 i. What is the...
discrete math
a. Consider the following rooted tree: 7 10 11 12 i. What is the root? (1 marks) ii. What is the height of the tree? (1 marks) iii. What are the children of the vertex 3? (1 marks) a. Draw the directed graph corresponding to the adjacency matrix (2 marks) [1 0 0 ON 1 2 1 b. Using the adjacency matrix in (a) only, determine the number of walks of length 3 from each vertex to each...
5. The in-degree of a vertex in a directed graph is the number of edges directed...
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...
3. The indegree of a vertex u is the number of incoming edges into u, .e, edges of the form (v,u)...
3. The indegree of a vertex u is the number of incoming edges into u, .e, edges of the form (v,u) for some vertex v Consider the following algorithm that takes the adjacency list Alvi, v2, n] of a directed graph G as input and outputs an array containing all indegrees. An adjacency list Alvi, v.. /n] is an array indexed by the vertices in the graph. Each entry Alv, contains the list of neighbors of v) procedure Indegree(Alvi, v2,......
For a directed graph the in-degree of a vertex is the number of edges it has...
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...
Consider a directed acyclic graph G = (V, E) without edge lengths and a start vertex...
Consider a directed acyclic graph G = (V, E) without edge lengths and a start vertex s E V. (Recall, the length of a path in an graph without edge lengths is given by the number of edges on that path). Someone claims that the following greedy algorithm will always find longest path in the graph G starting from s. path = [8] Ucurrent = s topologically sort the vertices V of G. forall v EV in topological order do...
114points Let G- (V,E) be a directed graph. The in-degree of a vertex v is the...
114points Let G- (V,E) be a directed graph. The in-degree of a vertex v is the number of edges (a) Design an algorithm (give pseudocode) that, given a vertex v EV, computes the in-degree of v under (b) Design an algorithm (give pseudocode) that, given a vertex v E V, computes the in-degree of v incident into v. the assumption that G is represented by an adjacency list. Give an analysis of your algorithm. under the assumption that G is...
Discrete math 1. Consider the graph on all two-element subsets of (a. b, c.d,e), in which...
Discrete math
1. Consider the graph on all two-element subsets of (a. b, c.d,e), in which two subsets are neighbors if they have a common element. Give a hamiltonian cycle in this graph. 2. Draw the line graph of Ksa. What is its chromatic munber? 3. Show that if G and H are two bipartite graphs, then the Cartesian product GxH is also bipartite.
1. Consider a directed graph with distinct and non-negative edge lengths and a source vertex s....
1. Consider a directed graph with distinct and non-negative edge lengths and a source vertex s. Fix a destination vertex t, and assume that the graph contains at least one s-t path. Which of the following statements are true? [Check all that apply.] ( )The shortest (i.e., minimum-length) s-t path might have as many as n−1 edges, where n is the number of vertices. ( )There is a shortest s-t path with no repeated vertices (i.e., a "simple" or "loopless"...
Given a directed graph with positive edge lengths and a specified vertex v in the graph,...
Given a directed graph with positive edge lengths and a
specified vertex v in the graph, the "all-pairs"
v-constrained shortest path problem" is the problem of computing
for each pair of vertices i and j the shortest
path from i to j that goes through the vertex
v. If no such path exists, the answer is
. Describe an algorithm that takes a graph G= (V; E) and vertex
v as input parameters and computes values L(i; j) that
represent...
Consider the following directed graph for each of the problems: 1. Perform a breadth-first search on...
Consider the following directed graph for each of the
problems:
1. Perform a breadth-first search on the graph assuming that the
vertices and adjacency lists
are listed in alphabetical order. Show the breadth-first search
tree that is generated.
2. Perform a depth-first search on the graph assuming that the
vertices and adjacency lists
are listed in alphabetical order. Classify each edge as tree, back
or cross edge. Label each
vertex with its start and finish time.
3. Remove all the...
discrete math
a. Consider the following rooted tree: 7 10 11 12 i. What is the root? (1 marks) ii. What is the height of the tree? (1 marks) iii. What are the children of the vertex 3? (1 marks) a. Draw the directed graph corresponding to the adjacency matrix (2 marks) [1 0 0 ON 1 2 1 b. Using the adjacency matrix in (a) only, determine the number of walks of length 3 from each vertex to each...
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...
3. The indegree of a vertex u is the number of incoming edges into u, .e, edges of the form (v,u) for some vertex v Consider the following algorithm that takes the adjacency list Alvi, v2, n] of a directed graph G as input and outputs an array containing all indegrees. An adjacency list Alvi, v.. /n] is an array indexed by the vertices in the graph. Each entry Alv, contains the list of neighbors of v) procedure Indegree(Alvi, v2,......
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...
Consider a directed acyclic graph G = (V, E) without edge lengths and a start vertex s E V. (Recall, the length of a path in an graph without edge lengths is given by the number of edges on that path). Someone claims that the following greedy algorithm will always find longest path in the graph G starting from s. path = [8] Ucurrent = s topologically sort the vertices V of G. forall v EV in topological order do...
114points Let G- (V,E) be a directed graph. The in-degree of a vertex v is the number of edges (a) Design an algorithm (give pseudocode) that, given a vertex v EV, computes the in-degree of v under (b) Design an algorithm (give pseudocode) that, given a vertex v E V, computes the in-degree of v incident into v. the assumption that G is represented by an adjacency list. Give an analysis of your algorithm. under the assumption that G is...
Discrete math
1. Consider the graph on all two-element subsets of (a. b, c.d,e), in which two subsets are neighbors if they have a common element. Give a hamiltonian cycle in this graph. 2. Draw the line graph of Ksa. What is its chromatic munber? 3. Show that if G and H are two bipartite graphs, then the Cartesian product GxH is also bipartite.
Given a directed graph with positive edge lengths and a
specified vertex v in the graph, the "all-pairs"
v-constrained shortest path problem" is the problem of computing
for each pair of vertices i and j the shortest
path from i to j that goes through the vertex
v. If no such path exists, the answer is
. Describe an algorithm that takes a graph G= (V; E) and vertex
v as input parameters and computes values L(i; j) that
represent...
Consider the following directed graph for each of the
problems:
1. Perform a breadth-first search on the graph assuming that the
vertices and adjacency lists
are listed in alphabetical order. Show the breadth-first search
tree that is generated.
2. Perform a depth-first search on the graph assuming that the
vertices and adjacency lists
are listed in alphabetical order. Classify each edge as tree, back
or cross edge. Label each
vertex with its start and finish time.
3. Remove all the...
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