Book edition 7th

Author(s) Kenneth H. Rosen

Pages 808 pages

ISBN 9780073383095

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Short Answer

Is a shortest path between two vertices in a weighted graph unique if the weights of edges are distinct?

The shortest path between two vertices need not be unique.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given data

The graph is given as,

Step 2: Concept used of Dijkstra’s algorithm

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

Step 3: Find the least path

Consider the graph shown below with vertices

\(A,B\) and \(C\) with weight \(AB = 1\), weight \({\rm{AC}} = 2\) and weight \(BC = 3\)

In this case the weights are distinct but there are two shortest paths from \(B\) to \(C\): the direct path \(B,C\) and the path through \({\rm{A:B,A,C}}\) both having the same length 3 .

This example shows that the shortest path between vertices need not be unique (even) if the weights are distinct.

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Discrete Mathematics and its Applications

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Short Answer

Is a shortest path between two vertices in a weighted graph unique if the weights of edges are distinct?

Step by Step Solution

Step 1: Given data

Step 2: Concept used of Dijkstra’s algorithm

Step 3: Find the least path

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Discrete Mathematics and its Applications

Answers without the blur.

Short Answer

Is a shortest path between two vertices in a weighted graph unique if the weights of edges are distinct?

Step by Step Solution

Step 1: Given data

Step 2: Concept used of Dijkstra’s algorithm

Step 3: Find the least path

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