An unlabeled graph is a graph in which individual nodes have no distinct identifications except through their interconnectivity. Graphs in which labels (which are most commonly numbers) are assigned to nodes are called labeled graphs. Unless indicated otherwise by context, the unmodified term "graph" generally refers to an unlabeled graph.

For a nonempty finite simple graph , its sibling number is the largest number of vertices sharing a closed neighborhood, minus one. Its tuft number is the largest number of pendant vertices adjacent to any one graph vertex. Among the unlabeled connected graphs of a fixed positive order , these statistics have a symmetric joint distribution (Fürnsinn et al. 2026). In particular,

where each sum includes one representative of each graph isomorphism class.

See also

Graph, Labeled Graph, Simple Graph

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References

Fürnsinn, F.; Gangl, M.; and Rubey, M. "Unexpectedly, a Symmetry on Unlabeled Graphs." Elec. J. Combin. 33, P4.32, 2026. https://doi.org/10.37236/15312.

Referenced on Wolfram|Alpha

Unlabeled Graph

Cite this as:

Weisstein, Eric W. "Unlabeled Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/UnlabeledGraph.html

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