As far as I know, that a path of a simple graph will never contain repeated vertex or edges but when I was going through the Discrete Mathematics book by Kenneth Rosen, "It says that a path in a directed graph can pass through a vertex more than once. Moreover, an edge in a directed graph can occur more than once in a path." Please clarify my doubt!
Can a path of a directed graph contain repeated vertex/edge?
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discrete-mathematics
graph-theory
1 Answers
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Note that many authors use slightly different definitions for a path, among other things, in graph theory. So your confusion may be cause by the fact that a path is often defined to only traverse vertices and edges once.
For clarification of what you ask, a simple graph $G$ contains no loops, so any path in $G$ cannot contain a repeated edge or vertex. In an arbitrary directed graph there may be cycles, hence edges and vertices may occur more than once.