Homework Answers
Topological ordering for Directed Acyclic Graph (DAG) is a linear ordering of vertices such that for every directed edge uv, vertex u comes before v in the ordering. Now if u look at the second option given in the ordering:
f , a , b , d , e , c.
This shows that b is before e but since there is a directed edge from e to b e should come before b , therefore this option is false.
For the 4th question , definition of a flow is given as :
A flow network is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. A flow must satisfy the restriction that the amount of flow into a node equals the amount of flow out of it, unless it is a source, which has only outgoing flow, or sink, which has only incoming flow.
Therefore source has only outgoing flow which means flow out of source > 0. So first option is not part of definition of flow.
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Which of the following is not a topological ordering for the graph: A ) O f, e, d, a, c, b O f, a, b, d, e, c O e, f, a, d, c, b O f,a,c,e,d,b QUESTION 4 Which of the following is not part of the def...
1. In the following graph, suppose that the vertices A, B, C, D, E, and F represent towns, and th...
question 1 and 2 please, thank
you.
1. In the following graph, suppose that the vertices A, B, C, D, E, and F represent towns, and the edges between those vertices represent roads. And suppose that you want to start traveling from town A, pass through each town exactly once, and then end at town F. List all the different paths that you could take Hin: For instance, one of the paths is A, B, C, E, D, F. (These...
a. b. c. d. e. What are the vertices? Is this graph connected? What is the...
a. b. c. d. e. What are the vertices? Is this graph connected? What is the degree of vertex C? Edge FE is adjacent to which edges? Does this graph have any bridges? Answer the following questions based on the graph below. 1w a. b. c. d. What are the vertices? What is the degree of vertex u? What is the degree of vertex s? What is one circuit in the graph?
6. Prove that the following graphs are connected: (a) The 3 vertex cycle: (b) The following 4 vertex graph: (c) K 7. An edge e of a connected graph G is called a cut edge if the graph G obtained by d...
6. Prove that the following graphs are connected: (a) The 3 vertex cycle: (b) The following 4 vertex graph: (c) K 7. An edge e of a connected graph G is called a cut edge if the graph G obtained by deleting that edge (V(G) V(G) and E(G) E(G) \<ej) is not connected. Prove that if G1 and G2 are connected simple graphs which are isomorphic and if G1 has a cut edge, then G2 also has a cut edge....
File Edit Format View Help Graphs and trees 4. [6 marks] Using the following graph representation (G(V,E,w)): v a,b,c,d,e,f E fa,b), (a,f),fa,d), (b,e), (b,d), (c,f),(c,d),(d,e),d,f)) W(a,b) 4,...
File Edit Format View Help Graphs and trees 4. [6 marks] Using the following graph representation (G(V,E,w)): v a,b,c,d,e,f E fa,b), (a,f),fa,d), (b,e), (b,d), (c,f),(c,d),(d,e),d,f)) W(a,b) 4,W(a,f) 9,W(a,d) 10 W(b,e) 12,W(b,d) 7,W(c,d) 3 a) Draw the graph including weights. b) Given the following algorithm for Inding a minimum spanning tree for a graph: Given a graph (G(V,E)) create a new graph (F) with nodes (V) and no edges Add all the edges (E) to a set S and order them...
Help with Q3 please! 3 (9 pts) For the graph G (VE) in question 2 (above),...
Help with Q3 please!
3 (9 pts) For the graph G (VE) in question 2 (above), construct the adjacency lists for G (using alphabetical ordering) and the corresponding reverse graph GR Adjacency list for G (alphabetical ordering): Adjacency list for G. V = {A, B, C, D, G, H, S) V - {A, B, C, D, G, H, S) E A = { EB = EC) - E[D] = {C,G) E[G] - [ ECH - E[S { EA = {...
Question 1 V g(x) O a Let g)-IOdt, where asx Sb. The figure above shows the graph of g on [a.t]. Which of the following could be the graph of f on [a,b]? (B) y (A) Y 0 ct (E) Y D) Question 2 100 12 1...
Question 1 V g(x) O a Let g)-IOdt, where asx Sb. The figure above shows the graph of g on [a.t]. Which of the following could be the graph of f on [a,b]? (B) y (A) Y 0 ct (E) Y D) Question 2 100 12 18 24 Hours The flow of oil, in barrels per hour, through a pipeline on July 9 is given by the graph shown above. Of the following, which best approximates the total number of...
Hi, I could use some help for this problem for my discrete math class. Thanks! 18. Consider the graph G = (V, E) with vertex set V = {a, b, c, d, e, f, g} and edge set E = {ab, ac, af, bg, ca, ce) (h...
Hi, I could use some help for this problem for my discrete math
class. Thanks!
18. Consider the graph G = (V, E) with vertex set V = {a, b, c, d, e, f, g} and edge set E = {ab, ac, af, bg, ca, ce) (here we're using some shorthand notation where, for instance, ab is an edge between a and b). (a) (G1) Draw a representation of G. (b) (G2) Is G isomorphic to the graph H -(W,F)...
D Question 1 2 pts Which Graph Algorithm (as described in lecture) relies on a Priority Queue to ...
Graph Question
D Question 1 2 pts Which Graph Algorithm (as described in lecture) relies on a Priority Queue to give it maximum efficiency? Prim's Algorithm ⓔ Dijkstra's Algorithm Kuemmel-Deppeler Algorithm Topological Ordering Algorithm Kruskal's Algorithm D Question 7 2 pts At the beginning of the Dijkstra's Algorithm, which of the following must be done? Select all correct choices. set all total weights to O mark all vertices as unvisited O sort all edges set all predecessors to null
D...
Question 1 part a, d, e, f, g, h Construct and plot the network using the...
Question 1 part a, d, e, f, g, h
Construct and plot the network using the igraph package
http://igraph.org/redirect.html and the adjacency list you
wrote.
To assign vertex names you can write it as
g = graph(edges = c("a", "b", "b", "c"), directed =
FALSE)
or
g = graph(edges = c(1, 2, 2, 3), directed = FALSE)
V(g)$name = c("a", "b", "c")
1. Answer the following questions about this graph. a. What is the degree distribution for th graph? b....
(c) Simulate breadth first search on the graph shown in Fig HW2Q1c. You can assume that...
(c) Simulate breadth first search on the graph shown in Fig
HW2Q1c. You can assume that the starting vertex is 1, and the
neighbors of a vertex are examined in increasing numerical order
(i.e. if there is a choice between two or more neighbors, we pick
the smaller one). You have to show: both the order in which the
vertices are visited and the breadth first search tree. No
explanations necessary.
(d) On the same graph, i.e. the graph in...
question 1 and 2 please, thank
you.
1. In the following graph, suppose that the vertices A, B, C, D, E, and F represent towns, and the edges between those vertices represent roads. And suppose that you want to start traveling from town A, pass through each town exactly once, and then end at town F. List all the different paths that you could take Hin: For instance, one of the paths is A, B, C, E, D, F. (These...
a. b. c. d. e. What are the vertices? Is this graph connected? What is the degree of vertex C? Edge FE is adjacent to which edges? Does this graph have any bridges? Answer the following questions based on the graph below. 1w a. b. c. d. What are the vertices? What is the degree of vertex u? What is the degree of vertex s? What is one circuit in the graph?
6. Prove that the following graphs are connected: (a) The 3 vertex cycle: (b) The following 4 vertex graph: (c) K 7. An edge e of a connected graph G is called a cut edge if the graph G obtained by deleting that edge (V(G) V(G) and E(G) E(G) \<ej) is not connected. Prove that if G1 and G2 are connected simple graphs which are isomorphic and if G1 has a cut edge, then G2 also has a cut edge....
File Edit Format View Help Graphs and trees 4. [6 marks] Using the following graph representation (G(V,E,w)): v a,b,c,d,e,f E fa,b), (a,f),fa,d), (b,e), (b,d), (c,f),(c,d),(d,e),d,f)) W(a,b) 4,W(a,f) 9,W(a,d) 10 W(b,e) 12,W(b,d) 7,W(c,d) 3 a) Draw the graph including weights. b) Given the following algorithm for Inding a minimum spanning tree for a graph: Given a graph (G(V,E)) create a new graph (F) with nodes (V) and no edges Add all the edges (E) to a set S and order them...
Help with Q3 please!
3 (9 pts) For the graph G (VE) in question 2 (above), construct the adjacency lists for G (using alphabetical ordering) and the corresponding reverse graph GR Adjacency list for G (alphabetical ordering): Adjacency list for G. V = {A, B, C, D, G, H, S) V - {A, B, C, D, G, H, S) E A = { EB = EC) - E[D] = {C,G) E[G] - [ ECH - E[S { EA = {...
Question 1 V g(x) O a Let g)-IOdt, where asx Sb. The figure above shows the graph of g on [a.t]. Which of the following could be the graph of f on [a,b]? (B) y (A) Y 0 ct (E) Y D) Question 2 100 12 18 24 Hours The flow of oil, in barrels per hour, through a pipeline on July 9 is given by the graph shown above. Of the following, which best approximates the total number of...
Hi, I could use some help for this problem for my discrete math
class. Thanks!
18. Consider the graph G = (V, E) with vertex set V = {a, b, c, d, e, f, g} and edge set E = {ab, ac, af, bg, ca, ce) (here we're using some shorthand notation where, for instance, ab is an edge between a and b). (a) (G1) Draw a representation of G. (b) (G2) Is G isomorphic to the graph H -(W,F)...
Graph Question
D Question 1 2 pts Which Graph Algorithm (as described in lecture) relies on a Priority Queue to give it maximum efficiency? Prim's Algorithm ⓔ Dijkstra's Algorithm Kuemmel-Deppeler Algorithm Topological Ordering Algorithm Kruskal's Algorithm D Question 7 2 pts At the beginning of the Dijkstra's Algorithm, which of the following must be done? Select all correct choices. set all total weights to O mark all vertices as unvisited O sort all edges set all predecessors to null
D...
Question 1 part a, d, e, f, g, h
Construct and plot the network using the igraph package
http://igraph.org/redirect.html and the adjacency list you
wrote.
To assign vertex names you can write it as
g = graph(edges = c("a", "b", "b", "c"), directed =
FALSE)
or
g = graph(edges = c(1, 2, 2, 3), directed = FALSE)
V(g)$name = c("a", "b", "c")
1. Answer the following questions about this graph. a. What is the degree distribution for th graph? b....
(c) Simulate breadth first search on the graph shown in Fig
HW2Q1c. You can assume that the starting vertex is 1, and the
neighbors of a vertex are examined in increasing numerical order
(i.e. if there is a choice between two or more neighbors, we pick
the smaller one). You have to show: both the order in which the
vertices are visited and the breadth first search tree. No
explanations necessary.
(d) On the same graph, i.e. the graph in...
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