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An icosahedron is a polyhedron consisting of 20 equilateral triangles. (a) Determine the number of edges of an icosahedron. (b) Use Euler's Formula to determine the number of vertices of an i...
5. Let G is a simple planar graph containing no triangles. (i) Using Euler's formula, show...
5. Let G is a simple planar graph containing no triangles. (i) Using Euler's formula, show that G contains a vertex of degree at most 3. (ii) Use induction to deduce that G is 4-colorable-(v).
5. Let G is a simple planar graph containing no triangles. (i) Using Euler's formula, show that G contains a vertex of degree at most 3. (ii) Use induction to deduce that G is 4-colorable-(v).
Discrete Mathematics 6: A: Draw a graph with 5 vertices and the requisite number of edges...
Discrete Mathematics
6: A: Draw a graph with 5 vertices and the requisite number of edges to show that if four of the vertices have degree 2, it would be impossible for the 5 vertex to have degree 1. Repetition of edges is not permitted. (There may not be two different bridges connecting the same pair of vertices.) B: Draw a graph with 4 vertices and determine the largest number of edges the graph can have, assuming repetition of edges...
solve with steps 1. (20 points) True or false. Justify. Every planar graph is 4-colorable /2 The number of edges in a simple graph G is bounded by n(n 1) where n is the number of vertices. The number...
solve with steps
1. (20 points) True or false. Justify. Every planar graph is 4-colorable /2 The number of edges in a simple graph G is bounded by n(n 1) where n is the number of vertices. The number of edges of a simple connected graph G is at least n-1 where n is the number of vertices. Two graphs are isomorphic if they have the same number of vertices and 1) the same mumber of edges
1. (20 points)...
Given the directed graph with vertices(A, B, C, D, E, F, G, H, I) Edges (AB=5,...
Given the directed graph with vertices(A, B, C, D, E, F, G, H, I) Edges (AB=5, BF = 4, AC = 7, CD=3, EC = 4, DE = 5, EH = 2, HI = 4, GH = 10, GF = 3, IG = 3, BE = 2, HD= 7, EG= 9 1. What is the length of minimum spaning tree? 2. Which edges will not be included if we use Kruskal's algorithm to find minimum spaning tree?
Can you please solve this fully Question 9 (10 marks) (i) How many vertices and how many edges do each of the following graphs have? [3 marks] (b) C16 (a) K70 (d) K2,5 (ii Suppose you have a graph G w...
Can you please solve this
fully
Question 9 (10 marks) (i) How many vertices and how many edges do each of the following graphs have? [3 marks] (b) C16 (a) K70 (d) K2,5 (ii Suppose you have a graph G with vertices vi, v. vi7. Explain (clearly) how you would use the adjacency matrix A to find a. The number of paths from v to vir of length 12.12 marks] b. The length of a shortest path from vi to...
3. (a) Let Knbe the complete bipartite graph with n vertices in each part of its bipartition, where n 21. Determine the number of perfect matchings of Kn (b) A matching M in a graph Gis ca a mazi...
3. (a) Let Knbe the complete bipartite graph with n vertices in each part of its bipartition, where n 21. Determine the number of perfect matchings of Kn (b) A matching M in a graph Gis ca a mazimal matching if there exists no matching M' of G such that M is a proper subset of M' Prove that, for any graph G and any edges e,f of G which are not incident with a common vertex, there exists a...
Problem 13. (1 point) Use Green's theorem to evaluate [4(-y +y)dx +4(x + 2xy)] dy. where C is the rectangle with vertices (0, 0), (5, 0) (5, 2) and (0, 2). A.1-20 B. I 160 DEI 40 Problem...
Problem 13. (1 point) Use Green's theorem to evaluate [4(-y +y)dx +4(x + 2xy)] dy. where C is the rectangle with vertices (0, 0), (5, 0) (5, 2) and (0, 2). A.1-20 B. I 160 DEI 40
Problem 13. (1 point) Use Green's theorem to evaluate [4(-y +y)dx +4(x + 2xy)] dy. where C is the rectangle with vertices (0, 0), (5, 0) (5, 2) and (0, 2). A.1-20 B. I 160 DEI 40
Spectroscopic Analysis Unknown 1: Molecule Number a) Determine the empirical formula from the microanalysis data, showing...
Spectroscopic Analysis Unknown 1: Molecule Number a) Determine the empirical formula from the microanalysis data, showing your working: Empirical Formula b) Does the mass spectrum imply the molecular formula is the same as the empirical formula? Why/Why not? Molecular Formula c) Use the 'double bond equivalents' formula to determine the degree on unsaturation for this molecule: d) What structural information can you garner from the IR spectrum? e) What structural information can you garner from the 'H NMR spectrum? Specify...
Genetics Question 4 Part B [20 marks] You will use a deBruijn graph to assemble the 10bp circular genome from which the...
Genetics Question 4 Part B [20 marks] You will use a deBruijn graph to assemble the 10bp circular genome from which these short (7-mer) reads have been derived: Reads: GCAGGTA TAACCGC GTAACCG CCGCAGG AGGTAAC A) Break the reads into the 10 k-mers for k 3 that you can obtain from these reads and write them out next to the reads in your book. [5 marks B) Draw a deBruijn graph using the k-mers as the edges to connect k -...
Question 4 Part B [20 marks] deBruijn graph (7-mer) reads have been derived: You will use...
Question 4 Part B [20 marks] deBruijn graph (7-mer) reads have been derived: You will use a to assemble the 10bp circular genome from which these short Reads GCAGGTA ТААССGC GTAACCG CCGCAGG AGGTAAC Break the reads into the 10 k-mers for k = 3 that you can obtain from these reads and write them out next to the reads in your book. [5 marks] ii. Draw a deBruijn graph using the k-mers as the edges to connect k - 1...
5. Let G is a simple planar graph containing no triangles. (i) Using Euler's formula, show that G contains a vertex of degree at most 3. (ii) Use induction to deduce that G is 4-colorable-(v).
5. Let G is a simple planar graph containing no triangles. (i) Using Euler's formula, show that G contains a vertex of degree at most 3. (ii) Use induction to deduce that G is 4-colorable-(v).
Discrete Mathematics
6: A: Draw a graph with 5 vertices and the requisite number of edges to show that if four of the vertices have degree 2, it would be impossible for the 5 vertex to have degree 1. Repetition of edges is not permitted. (There may not be two different bridges connecting the same pair of vertices.) B: Draw a graph with 4 vertices and determine the largest number of edges the graph can have, assuming repetition of edges...
solve with steps
1. (20 points) True or false. Justify. Every planar graph is 4-colorable /2 The number of edges in a simple graph G is bounded by n(n 1) where n is the number of vertices. The number of edges of a simple connected graph G is at least n-1 where n is the number of vertices. Two graphs are isomorphic if they have the same number of vertices and 1) the same mumber of edges
1. (20 points)...
Can you please solve this
fully
Question 9 (10 marks) (i) How many vertices and how many edges do each of the following graphs have? [3 marks] (b) C16 (a) K70 (d) K2,5 (ii Suppose you have a graph G with vertices vi, v. vi7. Explain (clearly) how you would use the adjacency matrix A to find a. The number of paths from v to vir of length 12.12 marks] b. The length of a shortest path from vi to...
3. (a) Let Knbe the complete bipartite graph with n vertices in each part of its bipartition, where n 21. Determine the number of perfect matchings of Kn (b) A matching M in a graph Gis ca a mazimal matching if there exists no matching M' of G such that M is a proper subset of M' Prove that, for any graph G and any edges e,f of G which are not incident with a common vertex, there exists a...
Problem 13. (1 point) Use Green's theorem to evaluate [4(-y +y)dx +4(x + 2xy)] dy. where C is the rectangle with vertices (0, 0), (5, 0) (5, 2) and (0, 2). A.1-20 B. I 160 DEI 40
Problem 13. (1 point) Use Green's theorem to evaluate [4(-y +y)dx +4(x + 2xy)] dy. where C is the rectangle with vertices (0, 0), (5, 0) (5, 2) and (0, 2). A.1-20 B. I 160 DEI 40
Spectroscopic Analysis Unknown 1: Molecule Number a) Determine the empirical formula from the microanalysis data, showing your working: Empirical Formula b) Does the mass spectrum imply the molecular formula is the same as the empirical formula? Why/Why not? Molecular Formula c) Use the 'double bond equivalents' formula to determine the degree on unsaturation for this molecule: d) What structural information can you garner from the IR spectrum? e) What structural information can you garner from the 'H NMR spectrum? Specify...
Genetics Question 4 Part B [20 marks] You will use a deBruijn graph to assemble the 10bp circular genome from which these short (7-mer) reads have been derived: Reads: GCAGGTA TAACCGC GTAACCG CCGCAGG AGGTAAC A) Break the reads into the 10 k-mers for k 3 that you can obtain from these reads and write them out next to the reads in your book. [5 marks B) Draw a deBruijn graph using the k-mers as the edges to connect k -...
Question 4 Part B [20 marks] deBruijn graph (7-mer) reads have been derived: You will use a to assemble the 10bp circular genome from which these short Reads GCAGGTA ТААССGC GTAACCG CCGCAGG AGGTAAC Break the reads into the 10 k-mers for k = 3 that you can obtain from these reads and write them out next to the reads in your book. [5 marks] ii. Draw a deBruijn graph using the k-mers as the edges to connect k - 1...
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