ForgottenIndex
The sum of the cubes of the degrees.
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St000571via LabeledGraph✓ForgottenIndex(graph)The sum of the cubes of the degrees.Typed signatures
| Type | Package | Applies |
|---|---|---|
(labeled_graph) -> number | combinatorics | always |
Details
- Defined over
LabeledGraphas an expression in_x, evaluated by compute-engine — the definition IS the implementation. - Takes a
LabeledGraphand 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 St000571, the F-index. The graph with no vertices gives 0.
Definition
Epsil, as the implementation runs it.
on LabeledGraph, over _x
0 if _x[1] == 0 else Apply((n: integer) => Apply((edges: list<list<integer>>) => Apply(
(degrees: list<integer>) => Max(Sum(Map(Function(d *
d * d, d), degrees)), 0),
Map(
Function(Max(Sum(Map(Function((1 if e[1] == v else 0) +
(1 if e[2] == v else 0), e), edges)), 0), v),
Range(1, n),
),
), _x[2]), _x[1])Examples
Properties #
About
| Examples | 4 |
|---|---|
| Crosswalk | FindStat |