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

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The discussion revolves around determining whether specific sequences of vertices in a directed graph can form a walk, path, or circuit. The first sequence, a, b, c, e, cannot form any of these due to the lack of a direct connection from c to e. The second sequence, b, c, d, d, e, c, f, qualifies as a walk. The third sequence, a, b, c, f, g, a, is identified as both a walk and a circuit, while the fourth sequence, b, c, d, e, is categorized as a walk and a path. Clarification on the definitions of walk, path, and circuit is suggested for better understanding.
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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:
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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