Welcome to Murphman’s Amusement Park! A guest of the park would like to start at the Entrance, walk along each of the midway streets (colored in grey) exactly once, and then leave at the Exit. Note that the railroad tracks are colored purple and are not midway streets. a.Draw a graph in the box above corresponding to this guest’s situation, and determine whether or not the graph has an Eulerian circuit, and if so, give one. If it does not, then explain why not. If the graph does not have an Eulerian circuit, determine whether it has an Eulerian path, and if it does, give one. If it does not, then explain why not. b. Is it possible for the guest to start at the Entrance, walk along all of the midway streets (colored in grey) exactly once, and then leave at the Exit?
Welcome to Murphman’s Amusement Park! A guest of the park would like to start at
the Entrance, walk along each of the midway streets (colored in grey) exactly once, and
then leave at the Exit. Note that the railroad tracks are colored purple and are not
midway streets.
a.Draw a graph in the box above corresponding to this guest’s situation,
and determine whether or not the graph has an Eulerian circuit, and if so, give
one. If it does not, then explain why not. If the graph does not have an Eulerian
circuit, determine whether it has an Eulerian path, and if it does, give one. If it
does not, then explain why not.
b. Is it possible for the guest to start at the Entrance, walk along all
of the midway streets (colored in grey) exactly once, and then leave at the Exit?
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