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Discrete Mathematics and its Applications
Found in: Page 738
Discrete Mathematics and its Applications

Discrete Mathematics and its Applications

Book edition 7th
Author(s) Kenneth H. Rosen
Pages 808 pages
ISBN 9780073383095

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Short Answer

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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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Introduction

In graph theory, the shortest path problem is the problem of finding a path between two vertices in a graph such that the sum of the weights of its constituent edges is minimized.

Step 2: Find the shortest path

Let us take the shortest path from a to z that passes through say f first of all shortest path from a to f and a shortest path from f to z , then put them together. In order to find shortest path for each of them use Dijkstra’s algorithm.

Hence, put f to z together, to find the shortest path.

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Show that the chromatic number of a graph is less than or equal to \({\bf{n - i + 1}}\), where \({\bf{n}}\) is the number of vertices in the graph and \({\bf{i}}\) is the independence number of this graph.

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How many vertices and how many edges does the complete m-partite graph \({{\rm{K}}_{{{\rm{n}}_{\rm{1}}}{\rm{,}}{{\rm{n}}_{\rm{2}}}{\rm{,}}.......{\rm{,}}{{\rm{n}}_{\rm{m}}}}}\)have?
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