Can These Sequences Form a Walk, Path, or Circuit in the Digraph?

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SUMMARY

The discussion focuses on determining whether specific sequences of vertices in a directed graph (digraph) form a walk, path, or circuit. The sequences analyzed include: 1) a, b, c, e - which does not form any valid structure due to the lack of a connection from c to e; 2) b, c, d, d, e, c, f - which qualifies as a walk; 3) a, b, c, f, g, a - which is both a walk and a circuit; and 4) b, c, d, e - which is classified as a walk and a path. The definitions of walk, path, and circuit are essential for clarity.

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  • Understanding of directed graphs (digraphs)
  • Knowledge of graph theory terminology: walk, path, circuit
  • Familiarity with vertex connectivity in graphs
  • Basic skills in analyzing graph structures
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  • Study the definitions and properties of walks, paths, and circuits in directed graphs
  • Explore examples of directed graphs and practice identifying walks, paths, and circuits
  • Learn about graph traversal algorithms such as Depth-First Search (DFS) and Breadth-First Search (BFS)
  • Investigate applications of directed graphs in computer science and network theory
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Students studying graph theory, computer science enthusiasts, and anyone interested in understanding the properties of directed graphs and their applications.

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Homework Statement


Given the graph, determine if the following sequences form a walk, path and/or a circuit.
http://img843.imageshack.us/img843/5686/digraph.png
1. a, b, c, e
2. b, c, d, d, e, c, f
3. a, b, c, f, g, a
4. b, c, d, e

Homework Equations


The Attempt at a Solution


1. It's not possible for the vertices to form a walk, path, or a circuit in this configuration. There is no relation from c to e.
2. walk
3. walk, circuit
4. walk, path

Are these correct, or am I missing something. Thanks for any suggestions.
 
Last edited by a moderator:
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nicnicman said:

Homework Statement


Given the graph, determine if the following sequences form a walk, path and/or a circuit.
http://img843.imageshack.us/img843/5686/digraph.png
1. a, b, c, e
2. b, c, d, d, e, c, f
3. a, b, c, f, g, a
4. b, c, d, e


Homework Equations





The Attempt at a Solution


1. It's not possible for the vertices to form a walk, path, or a circuit in this configuration. There is no relation from c to e.
2. walk
3. walk, circuit
4. walk, path

Are these correct, or am I missing something. Thanks for any suggestions.

You should probably give the definitions of 'walk', 'path' and 'circuit' for a directed graph.
 
Last edited by a moderator:

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