Homework Answers
IIn explanation of 37 1st one is not
hamiltonian cycle.
Add Answer to:
True or False?
36. K5,7 has a spanning subtree. Here are four graphs, A, B, C,...
Question 4 10 pts Look at the weighted graph and choose the TRUE answers below (do...
Question 4 10 pts Look at the weighted graph and choose the TRUE answers below (do not choose any FALSE answers) 1 B 4 4 2 5 D E 4 F 7 The graph has a minimal spanning tree of weight more than 15 The graph has a minimal spanning tree of weight less than 18 The graph has a Hamiltonian circuit ☺ ☺ ☺ ☺ The graph has an Euler circuit This graph is bipartite.
Write down true (T) or false (F) for each statement. Statements are shown below If a...
Write down true (T) or false (F) for each statement. Statements are shown below If a graph with n vertices is connected, then it must have at least n − 1 edges. If a graph with n vertices has at least n − 1 edges, then it must be connected. If a simple undirected graph with n vertices has at least n edges, then it must contain a cycle. If a graph with n vertices contain a cycle, then it...
math 270A quiz 10 discrete structures Name: Spring 2020 Math 270A Quiz 10 (MFCS 5.1-6.1) Directions:...
math 270A quiz 10 discrete structures
Name: Spring 2020 Math 270A Quiz 10 (MFCS 5.1-6.1) Directions: Please complete each question to the best of your ability. Show work to get full credit. Partially correct work will receive partial credit. Lastly please box your answer. 1. (2 points) Are the following graphs isomorphic? Explain why or why not. 2. (3 points) Find a minimum weight spanning tree of the graph below (either highlight the edges that make up the MST, or...
b) Given the following graph: AC ACE CEG C- ACE Is this graph has an Euler...
b) Given the following graph: AC ACE CEG C- ACE Is this graph has an Euler cycle? Justify your answer. 12 marks] i) Use the breadth first search algorithm to find a spanning tree in the above h. Assume vertex A is the root and the vertices are ordered Show clearly each step of how the algorithm is performed and present your answer in a table with three columns, the first column is the number of steps, the second column...
You may assume there are exactly simple graphs with vertex set We were unable to transcribe...
You may assume there are exactly
simple graphs with vertex set
We were unable to transcribe this image1, 2, V3, ..., Unf D)Explain why there are exactly 2) simple grahs with vertex sein which every vertex has even degree. (Hint: Establish a bijection between from this set to the set of all graphs with vertex set {vi, , Vn-1)). 2) Prove that the probability that a randomly chosen simple graph with vertex set {vi,... . vn) wil have an Eulerian...
Question 5: [10pt total] Let G be the following graph: True for False: Which of the...
Question 5: [10pt total] Let G be the following graph: True for False: Which of the following statements are true about G? 5)a) (1pt] G is a directed graph: 5)f) [1pt] G is bipartite: 5)b) [1pt] G is a weighted graph: 5)g) (1pt] G has a leaf vertex: ......... 5)c) [1pt] G is a multi-graph: 5)h) [1pt] G is planar: 5)d) [1pt] G is a loop graph: 5)i) [1pt] G is Eulerian: 5)) (1pt] G is a complete graph: 5)j)...
Write a c or c++ program to write a prims algorithm and for problem 2(b) use kruskal algorithm.
write a c or c++ program to write a prims algorithm and
for problem 2(b) use kruskal
algorithm.
Problem 2 (A) (Prim's Algorithm): Apply Prim's algorithm to the following graph. Include in the priority queue only the fringe vertices (the vertices not in the current tree which are adjacent to at least one tree vertex) Problem 2 (B) (Kruskal Algorithm): Apply Kruskaľ's algorithm to find a minimum spanning tree of the following graphs. 4 3 2 2 4 3 6...
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...
Q3.a) Show that every planar graph has at least one vertex whose degree is s 5. Use a proof by contradiction b) Using the above fact, give an induction proof that every planar graph can be colored...
Q3.a) Show that every planar graph has at least one vertex whose degree is s 5. Use a proof by contradiction b) Using the above fact, give an induction proof that every planar graph can be colored using at most six colors. c) Explain what a tree is. Assuming that every tree is a planar graph, show that in a tree, e v-1. Hint: Use Euler's formula
Q3.a) Show that every planar graph has at least one vertex whose degree...
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)...
Question 4 10 pts Look at the weighted graph and choose the TRUE answers below (do not choose any FALSE answers) 1 B 4 4 2 5 D E 4 F 7 The graph has a minimal spanning tree of weight more than 15 The graph has a minimal spanning tree of weight less than 18 The graph has a Hamiltonian circuit ☺ ☺ ☺ ☺ The graph has an Euler circuit This graph is bipartite.
math 270A quiz 10 discrete structures
Name: Spring 2020 Math 270A Quiz 10 (MFCS 5.1-6.1) Directions: Please complete each question to the best of your ability. Show work to get full credit. Partially correct work will receive partial credit. Lastly please box your answer. 1. (2 points) Are the following graphs isomorphic? Explain why or why not. 2. (3 points) Find a minimum weight spanning tree of the graph below (either highlight the edges that make up the MST, or...
b) Given the following graph: AC ACE CEG C- ACE Is this graph has an Euler cycle? Justify your answer. 12 marks] i) Use the breadth first search algorithm to find a spanning tree in the above h. Assume vertex A is the root and the vertices are ordered Show clearly each step of how the algorithm is performed and present your answer in a table with three columns, the first column is the number of steps, the second column...
You may assume there are exactly
simple graphs with vertex set
We were unable to transcribe this image1, 2, V3, ..., Unf D)Explain why there are exactly 2) simple grahs with vertex sein which every vertex has even degree. (Hint: Establish a bijection between from this set to the set of all graphs with vertex set {vi, , Vn-1)). 2) Prove that the probability that a randomly chosen simple graph with vertex set {vi,... . vn) wil have an Eulerian...
Question 5: [10pt total] Let G be the following graph: True for False: Which of the following statements are true about G? 5)a) (1pt] G is a directed graph: 5)f) [1pt] G is bipartite: 5)b) [1pt] G is a weighted graph: 5)g) (1pt] G has a leaf vertex: ......... 5)c) [1pt] G is a multi-graph: 5)h) [1pt] G is planar: 5)d) [1pt] G is a loop graph: 5)i) [1pt] G is Eulerian: 5)) (1pt] G is a complete graph: 5)j)...
write a c or c++ program to write a prims algorithm and
for problem 2(b) use kruskal
algorithm.
Problem 2 (A) (Prim's Algorithm): Apply Prim's algorithm to the following graph. Include in the priority queue only the fringe vertices (the vertices not in the current tree which are adjacent to at least one tree vertex) Problem 2 (B) (Kruskal Algorithm): Apply Kruskaľ's algorithm to find a minimum spanning tree of the following graphs. 4 3 2 2 4 3 6...
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...
Q3.a) Show that every planar graph has at least one vertex whose degree is s 5. Use a proof by contradiction b) Using the above fact, give an induction proof that every planar graph can be colored using at most six colors. c) Explain what a tree is. Assuming that every tree is a planar graph, show that in a tree, e v-1. Hint: Use Euler's formula
Q3.a) Show that every planar graph has at least one vertex whose degree...
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)...
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