Description
Return bound-degree and whether degree strictly exceeds the bound.
A graph's degree records how many edge incidences meet a vertex. Directed edges distinguish incoming and outgoing incidences, while loops and parallel edges require explicit counting conventions; a local degree formula does not reconstruct a graph.
Return bound-degree and whether degree strictly exceeds the bound.
When to use this tool
Use Vertex Deficiency From Bound when you need a degree or incidence calculation under the stated graph convention.
How to use the tool and how it works
- Enter degree, suppliedBound. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read deficiency, exceedsBound. Inspect exceedsBound before interpreting the associated values.
Require nonnegative integer degree and suppliedBound. Return bound-degree and whether degree strictly exceeds the bound.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| degree | Degree | Required. Safe integer; minimum 0. |
| suppliedBound | Supplied Bound | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| deficiency | Deficiency | Required. Safe integer. |
| exceedsBound | Exceeds Bound | Required. Boolean. |
{
"input": {
"degree": 3,
"suppliedBound": 5
},
"output": {
"deficiency": 2,
"exceedsBound": false
}
}Limitations and assumptions
- A negative deficiency is retained; the bound is supplied and no theorem assumptions, graph degree, or structural constraint is independently established.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Build an adjacency structure and count actual incidences when a full graph is available. Validate loop, multiplicity, direction, and vertex-set assumptions before applying a simple-graph identity.
References
Similar or alternative tools
- Graph Degree Sequence Single Node Budget
Return nodes-1-degree as remainingNeighbors and feasible when degree is below nodes.
- Graph Vertex Split Degree Balance
Assign the remaining stubs to the right and add one to each new degree only when connectingEdge; return the resulting totalDegree.