InducedPathOnThreeVerticesCount
The sets of three vertices that induce a path: exactly two of the three edges.
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St001308via LabeledGraph✓InducedPathOnThreeVerticesCount(graph)The sets of three vertices that induce a path: exactly two of the three edges.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 St001308. 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(
(adjacency: list<list<integer>>) => Max(Sum(Map(
Function(Max(Sum(Map(Function(Max(Sum(Map(Function((1 if u < w else 0) *
(1 if w < x else 0) *
(1 if adjacency[u][w] + adjacency[u][x] +
adjacency[w][x] ==
2 else 0), x), Range(1, n))), 0), w), Range(1, n))), 0), u),
Range(1, n),
)), 0),
Map(Function(Map(
Function(Max(Sum(Map(Function((1 if e[1] == i else 0) *
(1 if e[2] == j else 0) +
(1 if e[1] == j else 0) *
(1 if e[2] == i else 0), e), edges)), 0), j),
Range(1, n),
), i), Range(1, n)),
), _x[2]), _x[1])Examples
Properties #
About
| Examples | 4 |
|---|---|
| Crosswalk | FindStat |