ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
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Power set
Hyperpower set sequence
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Subset algebra
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Graph
Definition D2731
Complete graph
Formulation 0
A D778: Graph $G = (X, \mathcal{E})$ is complete if and only if \begin{equation} \mathcal{E} = \mathcal{P}_2(X) \end{equation}
Formulation 1
A D778: Graph $G = (X, \mathcal{E})$ is complete if and only if \begin{equation} \forall \, x, y \in X \, (x \neq y \quad \implies \quad \{ x, y \} \in \mathcal{E}) \end{equation}