Labeled Graph

A labeled graph $G=(V,E)$ is a finite series of Vertices $V$ with a set of Edges $E$ of 2-Subsets of $V$. Given a Vertex set $V_n=\{1$, 2, ..., $n\}$, the number of labeled graphs is given by $2^{n(n-1)/2}$. Two graphs $G$ and $H$ with Vertices $V_n=\{1, 2, \ldots, n\}$ are said to be Isomorphic if there is a Permutation $p$ of $V_n$ such that $\{u, v\}$ is in the set of Edges $E(G)$ Iff $\{p(u), p(v)\}$ is in the set of Edges $E(H)$.

See also Connected Graph, Graceful Graph, Graph (Graph Theory), Harmonious Graph, Magic Graph, Taylor's Condition, Weighted Tree

References

Cahit, I. ``Homepage for the Graph Labelling Problems and New Results.'' http://193.140.42.134/~cahit/CORDIAL.html.

Gallian, J. A. ``Graph Labelling.'' Elec. J. Combin. DS6, 1-43, Mar. 5, 1998. http://www.combinatorics.org/Surveys/.