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mathematics
contemporary mathematics

Questions and Answers of Contemporary Mathematics

\(x\) ! Hamilton cycles Given the number of Hamilton cycles in a complete graph, determine the number of vertices.
1. \(b \rightarrow a \rightarrow c \rightarrow d \rightarrow b\)2. \(b \rightarrow a \rightarrow d \rightarrow c \rightarrow b\)3. \(b \rightarrow c \rightarrow a \rightarrow d \rightarrow b\)4. \(b
1. \(i \rightarrow f \rightarrow g \rightarrow h \rightarrow e \rightarrow i\)2. \(i \rightarrow f \rightarrow g \rightarrow e \rightarrow h \rightarrow i\)3. \(i \rightarrow f \rightarrow h
\(q \rightarrow r \rightarrow s \rightarrow v \rightarrow y \rightarrow x \rightarrow w \rightarrow t \rightarrow u \rightarrow q\)Use the figure to find the weight of the given Hamilton cycle. 13 3
\(u \rightarrow y \rightarrow x \rightarrow w \rightarrow t \rightarrow q \rightarrow r \rightarrow s \rightarrow v \rightarrow u\)Use the figure to find the weight of the given Hamilton cycle. 13 3
\(y \rightarrow v \rightarrow s \rightarrow r \rightarrow u \rightarrow q \rightarrow t \rightarrow w \rightarrow x \rightarrow y\)Use the figure to find the weight of the given Hamilton cycle. 13 3
\(u \rightarrow v \rightarrow s \rightarrow r \rightarrow q \rightarrow t \rightarrow w \rightarrow x \rightarrow y \rightarrow u\)Use the figure to find the weight of the given Hamilton cycle. 13 3
The neighborhood of Pines West has three cul-de-sacs that meet at an intersection as shown. A postal delivery person starts at the intersection and visits each house in a cul-de-sac once, returns to
In chess, a knight can move in any direction, but it must move two spaces then turn and move one more space. The 8 possible moves a knight can make from a given space are shown in the figure.A graph
Graph \(G: f \rightarrow b \rightarrow g \rightarrow e \rightarrow d \rightarrow c\)Use the figure to determine whether the sequence of vertices in the given graph is a Hamilton path, an Euler trail,
Graph \(G: g \rightarrow b \rightarrow f \rightarrow c \rightarrow d \rightarrow e\)Use the figure to determine whether the sequence of vertices in the given graph is a Hamilton path, an Euler trail,
Graph \(G: f \rightarrow b \rightarrow g \rightarrow d \rightarrow f \rightarrow c \rightarrow d \rightarrow e \rightarrow g\)Use the figure to determine whether the sequence of vertices in the given
Graph \(W: v \rightarrow w \rightarrow r \rightarrow s \rightarrow t \rightarrow o \rightarrow q\)Use the figure to determine whether the sequence of vertices in the given graph is a Hamilton path,
Graph \(W: s \rightarrow r \rightarrow w \rightarrow v \rightarrow q \rightarrow o \rightarrow t\)Use the figure to determine whether the sequence of vertices in the given graph is a Hamilton path,
Graph \(N: h \rightarrow i \rightarrow k \rightarrow n \rightarrow j \rightarrow h\)Use the figure to determine whether the sequence of vertices in the given graph is a Hamilton path, an Euler trail,
Graph \(N: n \rightarrow i \rightarrow h \rightarrow j \rightarrow m\)Use the figure to determine whether the sequence of vertices in the given graph is a Hamilton path, an Euler trail, both, or
Graph \(N: m \rightarrow j \rightarrow h \rightarrow i \rightarrow k \rightarrow n \rightarrow i \rightarrow j \rightarrow k\)Use the figure to determine whether the sequence of vertices in the given
Graph \(A: t \rightarrow s \rightarrow v \rightarrow u \rightarrow x \rightarrow w \rightarrow y \rightarrow z\)Use the figure to explain why the given sequence of vertices does not represent a
Graph \(B: w \rightarrow x \rightarrow r \rightarrow u \rightarrow z \rightarrow y \rightarrow s \rightarrow t \rightarrow u \rightarrow v\)Use the figure to explain why the given sequence of
Graph \(C: s \rightarrow u \rightarrow w \rightarrow v \rightarrow t\)Use the figure to explain why the given sequence of vertices does not represent a Hamilton path. W Graph A X Graph B W S W Graph
Graph \(D: r \rightarrow \rightarrow t q \rightarrow u \rightarrow t \rightarrow x \rightarrow v \rightarrow w \rightarrow x \rightarrow z \rightarrow y\)Use the figure to explain why the given
A Hamilton path in Graph \(H\) that begins at vertex \(c\) and ends at vertex \(e\).Use the figure to find a path that fits the description or indicate which scenario from the figure makes it
A Hamilton path in Graph \(Q\) that begins at vertex \(n\) and ends at vertex \(h\).Use the figure to find a path that fits the description or indicate which scenario from the figure makes it
A Hamilton path in Graph \(H\) that begins at vertex \(c\) and ends at vertex \(g\).Use the figure to find a path that fits the description or indicate which scenario from the figure makes it
A Hamilton path in Graph \(Q\) that begins at vertex \(m\) and ends at vertex \(j\).Use the figure to find a path that fits the description or indicate which scenario from the figure makes it
A Hamilton path in Graph \(H\) that begins at vertex \(g\).Use the figure to find a path that fits the description or indicate which scenario from the figure makes it impossible. a C e Graph H Graph
A Hamilton path in Graph \(Q\) that begins at vertex \(i\).Use the figure to find a path that fits the description or indicate which scenario from the figure makes it impossible. a C e Graph H Graph
A path between \(n\) and \(j\) in Graph \(Q\) that is NOT a Hamilton path, and explain why it is not a Hamilton path.Use the figure to find a path that fits the description or indicate which scenario
A path between \(a\) and \(c\) in Graph \(H\) that is NOT a Hamilton path, and explain why it is not a Hamilton path.Use the figure to find a path that fits the description or indicate which scenario
In chess, a knight can move in any direction, but it must move two spaces then turn and move one more space. The eight possible moves a knight can make from a given space are shown in the figure.A
Draw a graph in which the vertices represent checkpoints, and an edge indicates that it is possible to travel from one checkpoint to the next without passing through another checkpoint.
Find a Hamilton path beginning at vertex \(A\) and ending at vertex \(E\).
What does this Hamilton path represent in the context of the race?
Draw a graph to represent the routes through the zoo in which the edges represent walkways and the vertices represent exhibits. Two vertices are connected if a person can walk between the exhibits
Use the graph you created to find a route that begins at exhibit \(M\), ends at exhibit \(J\), and visits each exhibit exactly once.The figure shows a map of zoo exhibits \(A\) through \(P\). Use it
The algorithm for creating graph colorings in the section Navigating Graphs involved coloring the vertex of highest degree first, coloring as many other vertices as possible each color from highest
Pallets of goods are to be transported on 10 flatbed trucks which have weight limits. To determine which goods will be shipped together, all the possible ways to divide the goods into 10 groups is
A wedding planner is creating a seating arrangement for the reception dinner. The couple has provided a list of which guests must be seated together. The wedding planner prefers to use the fewest
Packages must be loaded into freight cars to be transported by train. It is preferred to use the fewest freight cars possible to keep the costs down. As each freight car is packed, the package with
Graph \(A\), vertex \(a\)Use the figure to calculate the number of distinct Hamilton cycles beginning at the given vertex in the given graph. How many of those could possibly result in a different
Graph \(B\), vertex \(e\)Use the figure to calculate the number of distinct Hamilton cycles beginning at the given vertex in the given graph. How many of those could possibly result in a different
Graph \(C\), vertex \(k\)Use the figure to calculate the number of distinct Hamilton cycles beginning at the given vertex in the given graph. How many of those could possibly result in a different
Graph \(D\), vertex 0 Use the figure to calculate the number of distinct Hamilton cycles beginning at the given vertex in the given graph. How many of those could possibly result in a different
Graph \(A\), vertex \(a\)Use the figure to list all the distinct Hamilton cycles beginning at the given vertex in the given graph. Indicate which pairs of Hamilton cycles are reverses of each other.
Graph \(B\), vertex \(e\)Use the figure to list all the distinct Hamilton cycles beginning at the given vertex in the given graph. Indicate which pairs of Hamilton cycles are reverses of each other.
Graph \(C\), vertex \(k\)Use the figure to list all the distinct Hamilton cycles beginning at the given vertex in the given graph. Indicate which pairs of Hamilton cycles are reverses of each other.
Graph \(D\), vertex 0 Use the figure to list all the distinct Hamilton cycles beginning at the given vertex in the given graph. Indicate which pairs of Hamilton cycles are reverses of each other. - 2
Graph \(A\), vertex \(a\)Use the figure to find a Hamilton cycle of least weight for the given graph, beginning at the given vertex, and using the brute force method. What is the weight of the cycle?
Graph \(B\), vertex \(e\)Use the figure to find a Hamilton cycle of least weight for the given graph, beginning at the given vertex, and using the brute force method. What is the weight of the cycle?
Graph \(C\), vertex \(k\)Use the figure to find a Hamilton cycle of least weight for the given graph, beginning at the given vertex, and using the brute force method. What is the weight of the cycle?
Graph \(D\), vertex 0 Use the figure to find a Hamilton cycle of least weight for the given graph, beginning at the given vertex, and using the brute force method. What is the weight of the cycle? 12
Graph \(A\), vertex \(a\)Use the figure to find a Hamilton cycle of low weight for the given graph, beginning at the given vertex, and using the nearest neighbor method. What is the weight of the
Graph \(B\), vertex \(e\)Use the figure to find a Hamilton cycle of low weight for the given graph, beginning at the given vertex, and using the nearest neighbor method. What is the weight of the
Graph \(C\), vertex \(k\)Use the figure to find a Hamilton cycle of low weight for the given graph, beginning at the given vertex, and using the nearest neighbor method. What is the weight of the
Graph \(D\), vertex \(o\)Use the figure to find a Hamilton cycle of low weight for the given graph, beginning at the given vertex, and using the nearest neighbor method. What is the weight of the
Graph \(A\), vertex a Use your solutions to Exercises 13-20 to compare the results of the brute force method to the results of the nearest neighbor method for each graph. Indicate whether the
Graph \(B\), vertex \(e\)Use your solutions to Exercises 13-20 to compare the results of the brute force method to the results of the nearest neighbor method for each graph. Indicate whether the
Graph \(C\), vertex \(k\)Use your solutions to Exercises 13-20 to compare the results of the brute force method to the results of the nearest neighbor method for each graph. Indicate whether the
Graph \(D\), vertex \(o\)Use your solutions to Exercises 13-20 to compare the results of the brute force method to the results of the nearest neighbor method for each graph. Indicate whether the
\(U, V, W, X\)Use the table to create a complete weighted graph in which the vertices are the given cities, and the weights are the distances between them. Cities U V W X Y Z U 0 89 37 49 44 54 28 28
\(U, W, Y, Z\)Use the table to create a complete weighted graph in which the vertices are the given cities, and the weights are the distances between them. Cities U V W X Y Z U 0 89 37 49 44 54 28 28
\(U, X, Y, Z\)Use the table to create a complete weighted graph in which the vertices are the given cities, and the weights are the distances between them. Cities U V W X Y Z U 0 89 37 49 44 54 28 28
\(U, V, W, X, Y\)Use the table to create a complete weighted graph in which the vertices are the given cities, and the weights are the distances between them. Cities U V W X Y Z U 0 89 37 49 44 54 28
\(U, W, X, Y, Z\)Use the table to create a complete weighted graph in which the vertices are the given cities, and the weights are the distances between them. Cities U V W X Y Z U 0 89 37 49 44 54 28
\(U, V, W, X, Y, Z\)Use the table to create a complete weighted graph in which the vertices are the given cities, and the weights are the distances between them. Cities U V W X Y Z U 0 89 37 49 44 54
\(U, V, W, X\)Use your solutions to Exercises 25-30 and the nearest neighbor method to find a Hamilton cycle to solve the traveling salesperson problem of finding a reasonably short route to leave
\(U, W, Y, Z\)Use your solutions to Exercises 25-30 and the nearest neighbor method to find a Hamilton cycle to solve the traveling salesperson problem of finding a reasonably short route to leave
\(U, X, Y, Z\)Use your solutions to Exercises 25-30 and the nearest neighbor method to find a Hamilton cycle to solve the traveling salesperson problem of finding a reasonably short route to leave
\(U, V, W, X, Y\)Use your solutions to Exercises 25-30 and the nearest neighbor method to find a Hamilton cycle to solve the traveling salesperson problem of finding a reasonably short route to leave
\(U, W, X, Y, Z\)Use your solutions to Exercises 25-30 and the nearest neighbor method to find a Hamilton cycle to solve the traveling salesperson problem of finding a reasonably short route to leave
\(U, V, W, X, Y, Z\)Use your solutions to Exercises 25-30 and the nearest neighbor method to find a Hamilton cycle to solve the traveling salesperson problem of finding a reasonably short route to
\(U, V, W, X\)Use your solutions to Exercises \(25-30\) and the brute force method to find a Hamilton cycle of lowest weight to solve the traveling salesperson problem of finding a shortest route to
\(U, W, Y, Z\)Use your solutions to Exercises \(25-30\) and the brute force method to find a Hamilton cycle of lowest weight to solve the traveling salesperson problem of finding a shortest route to
\(U, X, Y, Z\)Use your solutions to Exercises \(25-30\) and the brute force method to find a Hamilton cycle of lowest weight to solve the traveling salesperson problem of finding a shortest route to
\(U, V, W, X, Y\)Use your solutions to Exercises \(25-30\) and the brute force method to find a Hamilton cycle of lowest weight to solve the traveling salesperson problem of finding a shortest route
\(U, W, X, Y, Z\)Use your solutions to Exercises \(25-30\) and the brute force method to find a Hamilton cycle of lowest weight to solve the traveling salesperson problem of finding a shortest route
Exercises 32 and \(38: U, W, Y, Z\)Use your solutions to the indicated exercises to compare the results of the brute force method to the results of the nearest neighbor method for each traveling
Exercises 31 and \(37: U, V, W, X\)Use your solutions to the indicated exercises to compare the results of the brute force method to the results of the nearest neighbor method for each traveling
Exercises 34 and \(40: U, V, W, X, Y\)Use your solutions to the indicated exercises to compare the results of the brute force method to the results of the nearest neighbor method for each traveling
Exercises 35 and \(41: U, W, X, Y, Z\)Use your solutions to the indicated exercises to compare the results of the brute force method to the results of the nearest neighbor method for each traveling
Exercises 33 and \(39: U, X, Y, Z\)Use your solutions to the indicated exercises to compare the results of the brute force method to the results of the nearest neighbor method for each traveling
\(A, C, D, F, G\)The products at a particular factory are manufactured in phases. The same equipment is utilized for each phase, but it must be formatted differently to accomplish different tasks.
\(B, D, E, F, G\)The products at a particular factory are manufactured in phases. The same equipment is utilized for each phase, but it must be formatted differently to accomplish different tasks.
\(A, B, C, D, E, F\)The products at a particular factory are manufactured in phases. The same equipment is utilized for each phase, but it must be formatted differently to accomplish different tasks.
\(B, C, D, E, F, G\)The products at a particular factory are manufactured in phases. The same equipment is utilized for each phase, but it must be formatted differently to accomplish different tasks.
\(A, B, C, D, E, F, G\)The products at a particular factory are manufactured in phases. The same equipment is utilized for each phase, but it must be formatted differently to accomplish different
\(A \rightarrow B \rightarrow F \rightarrow G \rightarrow K \rightarrow J \rightarrow F \rightarrow B\)Identify each sequence of vertices from the figure as a walk, trail, and/or path. Select all
\(G \rightarrow K \rightarrow O \rightarrow N \rightarrow J \rightarrow K \rightarrow L\)Identify each sequence of vertices from the figure as a walk, trail, and/or path. Select all that apply. A B D
\(F \rightarrow J \rightarrow K \rightarrow G \rightarrow B \rightarrow A\)Identify each sequence of vertices from the figure as a walk, trail, and/or path. Select all that apply. A B D E F G H I K L
\(I \rightarrow J \rightarrow K \rightarrow L \rightarrow K \rightarrow J \rightarrow N\)Identify each sequence of vertices from the figure as a walk, trail, and/or path. Select all that apply. A B D
\(M \rightarrow N \rightarrow O \rightarrow K \rightarrow L \rightarrow H\)Identify each sequence of vertices from the figure as a walk, trail, and/or path. Select all that apply. A B D E F G H I K L
\(A \rightarrow F \rightarrow K \rightarrow P\)Identify each sequence of vertices from the figure as a walk, trail, and/or path. Select all that apply. A B D E F G H I K L M N O P
\(N \rightarrow J \rightarrow F \rightarrow B \rightarrow C \rightarrow G \rightarrow F \rightarrow E\)Identify each sequence of vertices from the figure as a walk, trail, and/or path. Select all
\(E \rightarrow F \rightarrow J \rightarrow I \rightarrow E\)Identify each sequence of vertices from the figure as a walk, trail, and/or path. Select all that apply. A B D E F G H I K L M N O P
\(A \rightarrow B \rightarrow F \rightarrow G \rightarrow K \rightarrow J \rightarrow F \rightarrow B \rightarrow A\)Identify each sequence of vertices from Figure 12.134 as a closed walk, circuit
\(G \rightarrow K \rightarrow O \rightarrow N \rightarrow J \rightarrow K \rightarrow L\)Identify each sequence of vertices from Figure 12.134 as a closed walk, circuit (closed trail), and/or
\(F \rightarrow J \rightarrow N \rightarrow O \rightarrow K \rightarrow J \rightarrow I \rightarrow E \rightarrow F\)Identify each sequence of vertices from Figure 12.134 as a closed walk, circuit
\(I \rightarrow J \rightarrow K \rightarrow G \rightarrow F \rightarrow E \rightarrow I\)Identify each sequence of vertices from Figure 12.134 as a closed walk, circuit (closed trail), and/or
\(M \rightarrow N \rightarrow O \rightarrow K \rightarrow J \rightarrow I \rightarrow M\)Identify each sequence of vertices from Figure 12.134 as a closed walk, circuit (closed trail), and/or
\(N \rightarrow J \rightarrow F \rightarrow B \rightarrow C \rightarrow G \rightarrow F \rightarrow J \rightarrow N\)Identify each sequence of vertices from Figure 12.134 as a closed walk, circuit

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