66. m by n grid graphs . An m by n grid graph represents a rectangular street grid that is m . blocks by n blocks, as indicated in F i g . 6 - 5 1 . _ F i g u r e 6 - 5 1 a. If m and n are both odd, then the m by n grid graph has a Hamilton circuit. Describe the circuit by drawing it on a generic graph. b. If either m or n is even and the other one is odd, then the m by n grid graph has Hamilton circuit. Describe the circuit by drawing it on a generic graph. c. . If m and n are both even, then the m by n grid graph does not have a Hamilton circuit. Explain why a Hamilton circuit is impossible.
66. m by n grid graphs . An m by n grid graph represents a rectangular street grid that is m . blocks by n blocks, as indicated in F i g . 6 - 5 1 . _ F i g u r e 6 - 5 1 a. If m and n are both odd, then the m by n grid graph has a Hamilton circuit. Describe the circuit by drawing it on a generic graph. b. If either m or n is even and the other one is odd, then the m by n grid graph has Hamilton circuit. Describe the circuit by drawing it on a generic graph. c. . If m and n are both even, then the m by n grid graph does not have a Hamilton circuit. Explain why a Hamilton circuit is impossible.
Solution Summary: The author explains that a Hamilton circuit contains all the vertices of the graph exactly once except first and last vertex.
66. m by n grid graphs. An m by n grid graph represents a rectangular street grid that is m. blocks by n blocks, as indicated in
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a. If m and n are both odd, then the m by n grid graph has a Hamilton circuit. Describe the circuit by drawing it on a generic graph.
b. If either m or n is even and the other one is odd, then the m by n grid graph has Hamilton circuit. Describe the circuit by drawing it on a generic graph.
c. . If m and n are both even, then the m by n grid graph does not have a Hamilton circuit. Explain why a Hamilton circuit is impossible.
A. Find the number of vertices, the number of edges, and the degree of
each vertex of the following graphs below.
1.
2.
Q10C. Consider the graph with the following vertices and edges:
V = {a, b, c, d, e, f}
E = {{a, b}, {a, c}, {a, d}, {a, f}, {b, e}, {b, f}, {c, d}, {d, e}, {d, f}}
b
a
f
e
Which of the following are examples of circuits within the graph? (Select all that
apply.)
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