Description
Check the edge-count identity of a tree.
Graph and lattice counts depend on the allowed moves, edges and geometric or incidence assumptions. A necessary count identity or local conflict test may hold even when no valid complete object with the requested structure has been supplied.
Check the edge-count identity of a tree.
When to use this tool
Use Plane Tree Edge Vertex Balance when checking one supplied path, tree, matching or rook-placement condition.
How to use the tool and how it works
- Enter vertices, edges. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read residual, compatible. Inspect compatible before interpreting the associated values.
Check the edge-count identity of a tree. Require whole vertices >= 1 and edges >= 0; residual = edges-vertices+1, compatible means residual zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| vertices | Vertices | Required. Safe integer; minimum 1. |
| edges | Edges | Required. Safe integer; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residual | Signed difference in the direction stated above, with matching units. | Required. Safe integer. |
| compatible | Compatible | Required. Boolean. |
{
"input": {
"vertices": 7,
"edges": 6
},
"output": {
"residual": 0,
"compatible": true
}
}Limitations and assumptions
- The identity is necessary but does not prove connectivity, acyclicity, planarity or a valid supplied graph.
- 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
Inspect or construct the complete graph/path and apply all relevant structural constraints for a full validity or counting result.
References
Similar or alternative tools
- Catalan Triangulation Diagonal Budget
Return internal diagonal and triangle counts for a polygon triangulation.
- Hypergraph Uniform Edge Incidence Count Tool
Calculate hypergraph uniform edge incidence count from explicit caller-supplied inputs.