The title says it all. To reiterate:
What does one call an edge which is not a part of a cycle?
2026-05-17 16:37:50.1779035870
What does one call an edge which is not a part of a cycle?
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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.