IsTreeGraph

Whether a Graph is a tree — connected, with exactly $|V| - 1$ edges.

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IsTreeGraph(g)true iff

g

is connected (underlying, direction ignored) and has exactly

|V(g)| - 1

edges — the standard connected-plus-edge-count tree test.

Typed signatures

Type	Package	Applies
`(value) -> boolean`	`combinatorics`	always

Domain: Collections

Details

Wolfram calls this TreeGraphQ; this library uses the Is… spelling everywhere.

Examples

3 more kept as data, checked against the oracles

Basic #

\mathrm{IsTreeGraph}(\mathrm{StarGraph}(5))

Out

\mathrm{True}

One too many edges to be a tree

\mathrm{IsTreeGraph}(\mathrm{CycleGraph}(4))

Out

\mathrm{False}

Right edge count, but two components

\mathrm{IsTreeGraph}(\mathrm{Graph}(\bigl\lbrack1, 2, 3, 4\bigr\rbrack, \bigl\lbrack\mathrm{UndirectedEdge}(1, 2), \mathrm{UndirectedEdge}(3, 4)\bigr\rbrack))

Out

\mathrm{False}

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