Chapter 10: Q58SE (page 738)
Devise an algorithm for finding the shortest path between two vertices in a simple connected weighted graph that passes through a specified third vertex.
The shortest path is f to z together.
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The mathematics department has six committees, each
meeting once a month. How many different meeting times
must be used to ensure that no member is scheduled to
attend two meetings at the same time if the committees
are,
\(\begin{array}{*{20}{l}}\begin{array}{l}{C_1} = \{ \;Arlinghaus, Brand, Zaslavsky\;\} ,\\{C_2} = \{ \;Brand, Lee, Rosen\;\} ,\end{array}\\\begin{array}{l}{C_3} = \{ \;Arlinghaus, Rosen, Zaslavsky\;\} ,\\{C_4} = \{ \;Lee, Rosen, Zaslavsky\;\} ,\end{array}\\\begin{array}{l}{C_5} = \{ \;Arlinghaus, Brand\;\} ,\\{C_6} = \{ \;Brand, Rosen, Zaslavsky\;\} \end{array}\end{array}\)
A tournament is a simple directed graph such that if u and v are distinct vertices in the graph, exactly one of (u, v) and (v, u) is an edge of the graph.What is the sum of the in-degree and out-degree of a vertex in a tournament?
State the four-color theorem. Are there graphs that cannot be colored with four colors?
Determine whether the following graphs are self-converse.
a)
b)
To determine the shortest path in terms of lease rates between Boston and Los Angeles.
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