IsPathGraph

Whether a Graph is a simple path — a single chain of vertices, each joined once to the next.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguagePathGraphQ!↗

IsPathGraph(g)true iff g is simple (no self-loop, no repeated edge) and its underlying graph is a path.

Typed signatures

Type	Package	Applies
(value) -> boolean	combinatorics	always

Domain: Collections

Details

• Wolfram calls this PathGraphQ; this library uses the Is… spelling everywhere (see IsConnectedGraph's own note).

Examples

Basic #

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In$\mathrm{IsPathGraph}(\mathrm{Graph}(\bigl\lbrack1, 2, 3, 4\bigr\rbrack, \bigl\lbrack\mathrm{UndirectedEdge}(1, 2), \mathrm{UndirectedEdge}(2, 3), \mathrm{UndirectedEdge}(3, 4)\bigr\rbrack))$Out$\mathrm{True}$

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In$\mathrm{IsPathGraph}(\mathrm{CycleGraph}(4))$Out$\mathrm{False}$

Properties #

A single vertex is the trivial path

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In$\mathrm{IsPathGraph}(\mathrm{Graph}(\bigl\lbrack1\bigr\rbrack, \bigl\lbrack\bigr\rbrack))$Out$\mathrm{True}$

A $1\times4$ grid is a path on four vertices

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In$\mathrm{IsPathGraph}(\mathrm{GridGraph}(\bigl\lbrack1, 4\bigr\rbrack))$Out$\mathrm{True}$

Transposed dimensions give the same path

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In$\mathrm{IsPathGraph}(\mathrm{GridGraph}(\bigl\lbrack4, 1\bigr\rbrack))$Out$\mathrm{True}$

Trailing singleton dimensions leave it a path

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In$\mathrm{IsPathGraph}(\mathrm{GridGraph}(\bigl\lbrack1, 4, 1\bigr\rbrack))$Out$\mathrm{True}$

About

Examples	6
Checked against	Wolfram Language 5 agree1 differ
Crosswalk	Wolfram Language

See also: PathGraph, IsTreeGraph, IsAcyclicGraph