Description
Return eccentricity-radius and mark center for an exact zero gap.
A rooted tree organizes vertices by parent, children, and distance from a root. Root status changes local degree relationships, and height or leaf formulas assume the supplied structure really satisfies the tree model.
Return eccentricity-radius and mark center for an exact zero gap.
When to use this tool
Use Tree Center Eccentricity Explicit Gap when you need a local rooted-tree count or bound from supplied structural facts.
How to use the tool and how it works
- Enter eccentricity, radius. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read gap, center. Inspect center before interpreting the associated values.
Require nonnegative integer radius and eccentricity at least radius. Return eccentricity-radius and mark center for an exact zero gap.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| eccentricity | Eccentricity | Required. Safe integer. |
| radius | Radius in the common length unit, with its geometric role defined above. | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| gap | Difference on the stated unit and subtraction basis. | Required. Safe integer. |
| center | Center | Required. Boolean. |
{
"input": {
"eccentricity": 4,
"radius": 3
},
"output": {
"gap": 1,
"center": false
}
}Limitations and assumptions
- Supplied radius and eccentricity are not computed from graph distances; this checks their local relationship without establishing the actual graph center.
- 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
Traverse a verified tree to derive parent, depth, and leaf data directly. A formula using claimed degrees or depths cannot independently establish connectedness, acyclicity, or a valid root.
References
Similar or alternative tools
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