In the book titled Introduction to Graph theory by Douglas B West, he states the definition of a path as:
A path is a simple graph whose vertices can be ordered so that two vertices are adjacent if and only if they are consecutive in the list.
Most definitions of path that I've seen require the vertices to be distinct in the path i.e no repeated vertices. Is the above definition consistent with the no repeated vertices since when West says "can be ordered" he implies we have an ordered set?
For example, if we consider the standard 3 -cycle with edges: {xy, yz, zx}, then the following is not a path (xyzx) since it is not an "ordering" of the vertices?
Thanks!
Yes, you understand correctly. The cycle $(xyzx)$ is not an ordering of the vertices since $x$ is used twice, but $(xyz)$ or $(zxy)$ would be.