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Chapter 10: Q13E (page 716)

To determine the shortest path in terms of lease rates between Boston and Los Angeles.

Short Answer

Expert verified

The shortest path is Boston, Chicago, Los Angeles is of length \(2300\).

Step by step solution

01

Given data

The graph representing lease rates

02

Concept used of Dijkstra’s algorithm

Dijkstra's algorithm allows us to find the shortest path between any two vertices of a graph.

03

Find the shortest path

Any path from Boston must pass through Chicago or New York.

The path Boston, Chicago, Los Angeles is of length \(2300\).

The path Boston, Chicago, Dallas, Los Angeles is of length \(2800\) .

The path Boston, New York, Dallas, Los Angeles is of length \(2600\) .

So, the shortest path is Boston, Chicago, Los Angeles is of length \(2300\) .

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Most popular questions from this chapter

The distance between two distinct vertices\({{\bf{v}}_{\bf{1}}}\)and\({{\bf{v}}_{\bf{2}}}\)of a connected simple graph is the length (number of edges) of the shortest path between\({{\bf{v}}_{\bf{1}}}\)and\({{\bf{v}}_{\bf{2}}}\). The radius of a graph is the minimum over all vertices\({\bf{v}}\)of the maximum distance from\({\bf{v}}\)to another vertex. The diameter of a graph is the maximum distance between two distinct vertices. Find the radius and diameter of

a)\({{\bf{K}}_{\bf{6}}}\)

b)\({{\bf{K}}_{{\bf{4,5}}}}\)

c)\({{\bf{Q}}_{\bf{3}}}\)

d)\({{\bf{C}}_{\bf{6}}}\)

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Show that if the directed graph G is self-converse and H is a directed graph isomorphic to G, then H is also self-converse.

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In Exercises \({\rm{3 - 5}}\)determine whether two given graphs are isomorphic.
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