May 2024
Intermediate to advanced
687 pages
18h 35m
English
Content preview from Discrete Mathematical Structures by Pearson
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Topics in Graph Theory 10-45
10.15 SHORTEST PATH PROBLEMS
The problem of finding shortest distance connecting cities by road/rail network is of great
importance in view of reduction in cost as well as time. We shall discuss two algorithms to
determine the shortest distance between two designated vertices: one in a graph without weights
and other in weighted graphs.
10.15.1 Shortest Path in a Graph without Weights
In a loop-free graph G(V, E) without weights, the shortest path between two vertices u and v is
the one that uses the least number of edges. Two algorithms known as breadth-first search (BFS)
and back-tracking search (BTS) are discussed ...
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