traversability

[amathproblemthatneedsolve]

I believe the image below is traversable by a path: F>D>C>F>G>D>H>G>E>A>B>E>H>B>C Is this correct?



Also what's the reason for this being transverable if I may ask?

 

[Steven G]

Let me see if I understand this correctly. You think that you found a traversable path but you want to know what's the reason for this being traverable.

Assuming you really meant to write what you wrote I can't imagine how you found a traversable path without knowing what a traversable path is.

This leads me to believe that you did not come up with this path on your own.

Can you please post back telling us what a traversable path is and why you think the one you listed is correct?

 

[amathproblemthatneedsolve]

A network is traversable if there is a route that covers each edge once and once only. This means you do not draw over an edge more than once or lift your pencil off the circuit. I think the one listed is correct because I haven't taken my pencil off the circuit or drawn over an edge more than once.

 

[JeffM]

Node A, Even.

Node B. Even.

Node C. Odd.

Node D. Even.

Node E. Even.

Node F. Odd.

Node G. Even.

Node H. Even.

Node K. Even.

Exactly two odd nodes. Traversable.

To be traversable means no odd nodes or just two odd nodes. If there are two odd nodes, a traversable path must start at an odd node.

 

[pka]

I believe the image below is traversable by a path: F>D>C>F>G>D>H>G>E>A>B>E>H>B>C Is this correct?

View attachment 14583
Also what's the reason for this being transverable if I may ask?

This is usually called an Eulerian traceable graph It was proved in 1873 that a connected graph is traceable if and only if it has 0 or exactly two odd vertices. If it has to odd vertices the trace must begin at one and end at the other. This graph is such with vertices \(\displaystyle C~\&~F\)

 

[amathproblemthatneedsolve]

If I give lengths, let's say A-B 400m, A-E 350m, B-C 260m, E-H450m, E-B 270m, E-G 360m, H-G 160m, G-F 100m, F-C 280m, B-H 580m, C-D 470m, H-D 380m.
The quickest route from A to D would be A>E>G>D 990km ?

What's the best way to put this into a table?

 

[pka]

Now you are asking about the Travelling salesman problem.

 

[amathproblemthatneedsolve]

Now you are asking about the Travelling salesman problem.

So this means I'm right If I read this properly!