Isomorphic Graphs

Two Graphs which contain the same number of Vertices connected in the same way are said to be isomorphic. Formally, 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 $E(H)$.

References

Chartrand, G. ``Isomorphic Graphs.'' §2.2 in Introductory Graph Theory. New York: Dover, pp. 32-40, 1985.