ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Hyperpower set sequence
Hyperpower set
Hypersubset
Subset algebra
Subset structure
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Graph
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Path subgraph
Finite path subgraph
Graph connectivity relation
Graph connected component
Definition D5853
Set of connected graph components
Formulation 0
Let $G = (X, \mathcal{E})$ be a D2742: Finite path graph such that
(i) ${\leftrightarrow}$ is a D5851: Graph connectivity relation for $G$
The set of connected components for $G$ is the D180: Quotient set \begin{equation} X / { \leftrightarrow } = \{ \leftrightarrow(x) : x \in X \} \end{equation}
Formulation 1
Let $G = (X, \mathcal{E})$ be a D2742: Finite path graph such that
(i) ${\leftrightarrow}$ is a D5851: Graph connectivity relation for $G$
The set of connected components for $G$ is the D180: Quotient set \begin{equation} X / { \leftrightarrow } = \left\{ \{ y : (x, y) \in {\leftrightarrow} \} : x \in X \right\} \end{equation}