EulerFaceCount

The edges less the vertices plus 2: the faces of a connected planar graph.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt000450via LabeledGraph✓↗

EulerFaceCount(graph)The edges less the vertices plus 2: the faces of a connected planar graph.

Typed signatures

Type	Package	Applies
(labeled_graph) -> number	combinatorics	always

Domain: Graph statistics

Details

• Defined over LabeledGraph as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a LabeledGraph and nothing else — it reads values against their positions, or walks the orbits, so it needs the bijection. Applying it to a bare list is a type error, not a wrong answer.
• FindStat's St000450. The graph with no vertices gives 2, the formula as written.

Definition

Epsil, as the implementation runs it.

on LabeledGraph, over _x

Length(_x[2]) - _x[1] + 2

Examples

Basic #

the graph on 4 vertices with the edges 12, 23, 24 and 34

live ↗

In$\mathrm{EulerFaceCount}(\operatorname{LabeledGraph}((4,\bigl\lbrack\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack2, 3\bigr\rbrack, \bigl\lbrack2, 4\bigr\rbrack, \bigl\lbrack3, 4\bigr\rbrack\bigr\rbrack)))$Out$2$

Properties #

FindStat's value for ([],1)

live ↗

In$\mathrm{CombinatorialStat}(\operatorname{LabeledGraph}((1,\bigl\lbrack\bigr\rbrack)), \text{EulerFaceCount})$Out$1$

Known value · FindStat St000450

FindStat's value for ([],2)

live ↗

In$\mathrm{CombinatorialStat}(\operatorname{LabeledGraph}((2,\bigl\lbrack\bigr\rbrack)), \text{EulerFaceCount})$Out$0$

Known value · FindStat St000450

FindStat's value for ([],3)

live ↗

In$\mathrm{CombinatorialStat}(\operatorname{LabeledGraph}((3,\bigl\lbrack\bigr\rbrack)), \text{EulerFaceCount})$Out$-1$

Known value · FindStat St000450

About

Examples	4
Crosswalk	FindStat