may i know what is the difference between a path and a walk, they seem to be the same thing to me.

i classified a walk as abcdef where each alphabet represents a vertex but my tutor said that that is a path...

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- Feb 15th 2011, 04:13 AMalexandrabel90walk
may i know what is the difference between a path and a walk, they seem to be the same thing to me.

i classified a walk as abcdef where each alphabet represents a vertex but my tutor said that that is a path... - Feb 15th 2011, 06:49 AMSudharaka
Hi alexandrabel90,

A walk is a finite sequence of vertices and edges beginning and ending with a vertex. Here both vertices and edges could repeat.

A path is a walk with distinct vertices and edges with the starting vertex and end vertex. Also the starting and end vertex in a path must be distinct.

So by the definitions we can see that every path is a walk.

For a more detailed discription refer Glossary of graph theory - Wikipedia, the free encyclopedia - Feb 15th 2011, 07:12 AMPlato
There is no universal agreement on these terms.

One text book on graph theory has a hierarchy of terms: walk, a trail, and a path.

Ais a collection of successive adjacent edges.**walk**

Ais a walk in which all edges are distinct.**trail**

Ais a trail in which all vertices are distinct.**path**