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The title says it all. To reiterate:

What does one call an edge which is not a part of a cycle?

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  • $\begingroup$ One possible is a bridge $\endgroup$ Commented Feb 15, 2020 at 21:58
  • $\begingroup$ For a connected graph, "bridge". $\endgroup$
    – Blue
    Commented Feb 15, 2020 at 21:59
  • $\begingroup$ It depends. It could be a chord. If you specify what you mean, it could be another thing. $\endgroup$ Commented Feb 15, 2020 at 22:25

1 Answer 1

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In graph theory, we say that an edge $e$ is a cut edge if its removal causes the original graph to become disconnected.

If $G$ is a simple graph, then it can be shown that an edge $e$ is contained in a cycle if and only if $e$ is not a cut edge (or bridge). A full proof is provided here. Thus, we usually call edges that are not part of a cycle a cut edge or a bridge.

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