Graph theory path notation

Question

Is the following notation appropriate for denoting a path within a graph?

$P=\{ab, bc, ca, cd, da\}$

Answer 1

That is not good notation.

First a path is a sequence of edges, not a set of edges. This allows for the path to pass over an edge more than once, which is certainly allowable in the definition of a path in a graph.

Second, even if one presumes that you are mis-using set notation, and that your intention was indeed to list the edges one after another, in that case you have not listed the edges in order and in the correct orientation along the path, making it that much harder for the reader to parse your path. For example, it appears from your notation that $ca$ is followed on the path by $cd$ which is clearly impossible because they do not meet end to end, meaning that terminal vertex $a$ of the edge $ca$ does not match the initial vertex $c$ of the next edge $cd$.

I would suggest a more geometric notation like $$P = ab * bc * ca * ad * dc $$ Notice that I interchanged the last two edges in your list, and I reversed each of their orientations.

Answer 2

No, it isn't, insofar you are using {set} brackets there. If this is not intended, use (normal) brackets to avoid confusion. In a set, the order of elements is not given, and therefore your path wouldn't be well defined in most if not all cases.