For each item: (i) sketch the directed bipartite graph representing each permutation; (ii) use the graph to find the inverse of the permutation, and (iii) find the number of inversions in the permutation and its inverse. d. (6, 3, 7, 2, 5, 1, 4)

Q: Question 88 Suppose 1000 people enter a chess tournament. Use a rooted tree model of the tournament…

A: Solution

Q: Express each permutation as a product of disjoint cycles and find the orbits of each permutation

A: Given: 1234535241

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Q: (a) Draw a graph with nodes representing the numbers 1, 2, ⋯ , 10, in which two nodes are connected…

A: Here 10 nodes will be present.

Q: Write the permutation corresponding to R90 in the left regular representationof D4 in cycle form.

A:

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Q: 3. Use the Greedy and Edge-Picking algorithms to find the Hamiltonian cycle with the least total…

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Q: In (Z24, €) find the orders of the elements 3, 4, 6, 7, and 18.

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

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A: In Kruskal's algorithm, the edge with minimum weight is chosen first.

Q: 4) Use the given lattice to find all pairs of elements that generate Dg. (There are 12 pairs)

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Q: Find the order of each element in Z12-

A:

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Q: 7 The graph shows AABC and AA'B'C'. Which sequence of transformations will carry AABC onto AA'B'C' ?

A: topic - transformation of graph

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Q: Q3: Write down the chromatic polynomials of (i) the complete graph; (ii) the complete bipartite…

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Q: Exercise 14.6.11. Suppose a is an an even or odd permutation? n-cycle. How can you tell whether a is

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Q: In general, if (12 · · · k) is a cycle of length k and o is any permutation then o(12 ·.· k)o -1 =…

A: Given: T=(12.....k)

Q: a) What is the maximum possible order of an element in S,? Give an example of one of these elements.…

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Q: Given AJKL EAJ'K'L', describe a sequence of transformations that maps AJKL to AJ'K'L'. -4- K' K -6 4…

A: topic - translation

Q: Express each permutation as a product of disjoint cycles and find the orbits of each permutation…

A: To express the permutation 1, 4, 8, 71, 9, 6, 51, 5, 3, 2, 9 as a product of disjoint cycles…

Q: Express each permutation as a product of disjoint cycles and find the orbits of each permutation

A: Given that, Let p = 1  2  3  4  5   6  73  4  5  6  1   2  7  be a permutation Two cycles are said…

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Q: 30 20 15 25 35 50 5 18 60 45

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Q: D H

A: In postorder we must first go to left then right and after that data.

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Q: Express each permutation as a product of disjoint cycles and find the orbits of each permutation

A: In this permutation  1→12→3→24→5→4

Q: 4: Find possible orders of elements in the groups S3, S4, and S5.

A:

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Q: Find the largest possible order of an element in S7.

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Q: In the group of U(20) , the order of (13) = 4

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Q: Find the number of conjugacy classes of S4 and the number of elements in each of these classes

A: Here, S4 is the permutation group of order 24.Number of elements in S4 = {(1),(1 2),(1 3),(1 4),(2…

Q: Express each permutation as a product of disjoint cycles and find the orbits of each permutation

A: a)1234523415b)1234513542

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Q: Draw and label the final image of AABC after the given sequence of transformations. (-)-(->)-(x) A…

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Q: Construct the De Bruijn graph for the given sequences   BBBAAAAB; where k =3 ACGCGTCG; where k=3

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A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

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A: Given: