MinimalDominatingSetCount
The dominating sets that stop dominating when any vertex is dropped.
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St001302via LabeledGraph✓MinimalDominatingSetCount(graph)The dominating sets that stop dominating when any vertex is dropped.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 St001302. The graph with no vertices has the empty set, so 1.
Definition
Epsil, as the implementation runs it.
on LabeledGraph, over _x
1 if _x[1] == 0 else Apply((n: integer) => Apply((edges: list<list<integer>>) => Apply(
(inside: list<integer>) => Apply(
(totals: list<integer>) => Apply(
(toSet: list<list<integer>>) => Apply(
(dominating: list<integer>) => Max(Sum(Map(Function(dominating[m + 1] *
(1 if Max(Sum(Map(Function(dominating[m -
2 ^
(v - 1) +
1] if m %
2 ^ v >=
2 ^
(v - 1) else 0, v), Range(1, n))), 0) ==
0 else 0), m), Range(0, 2 ^ n -
1))), 0),
Map(Function(1 if Max(Sum(Map(Function((1 -
(1 if m %
2 ^ v >=
2 ^
(v - 1) else 0)) *
(1 if toSet[m + 1][v] ==
0 else 0), v), Range(1, n))), 0) ==
0 else 0, m), Range(0, 2 ^ n -
1)),
),
Map(
Function(Map(Function(Max(Sum(Map(Function((1 if e[1] == v else 0) *
(1 if m %
2 ^ e[2] >=
2 ^
(e[2] - 1) else 0) +
(1 if e[2] == v else 0) *
(1 if m %
2 ^ e[1] >=
2 ^
(e[1] - 1) else 0), e), edges)), 0), v), Range(1, n)), m),
Range(0, 2 ^ n -
1),
),
),
Map(
Function(Max(Sum(Map(Function(1 if m %
2 ^ v >=
2 ^
(v - 1) else 0, v), Range(1, n))), 0), m),
Range(0, 2 ^ n -
1),
),
),
Map(
Function(Max(Sum(Map(Function((1 if m %
2 ^ e[1] >=
2 ^
(e[1] - 1) else 0) *
(1 if m %
2 ^ e[2] >=
2 ^
(e[2] - 1) else 0), e), edges)), 0), m),
Range(0, 2 ^ n -
1),
),
), _x[2]), _x[1])Examples
Properties #
About
| Examples | 4 |
|---|---|
| Crosswalk | FindStat |