The graph with only one vertex and no edges is called the " trivial graph ".
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"' Trivial Graph Format "'( "'TGF "') is a simple text-based file format for describing node definitions, which map node IDs to labels, followed by a list of edges, which specify node pairs and an optional edge label.
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Typically, only nontrivial actions on trees are studied in Bass Serre theory since trivial graphs of groups do not carry any interesting algebraic information, although trivial actions in the above sense ( e . g . actions of groups by automorphisms on rooted trees ) may also be interesting for other mathematical reasons.
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