Description
Invoke the linked join increment calculator for both original and added vertices.
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.
Invoke the linked join increment calculator for both original and added vertices.
When to use this tool
Use Graph Join Isolated Node Degree Shift when you need a degree or incidence calculation under the stated graph convention.
How to use the tool and how it works
- Enter originalDegree, originalOrder, isolatedGroupSize. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read originalVertexDegree, addedVertexDegree. Use the output convention below.
Require positive originalOrder and isolatedGroupSize and originalDegree within a simple original graph's range. Invoke the linked join increment calculator for both original and added vertices.1
The linked join-degree operation is called for both the original vertex and an added isolated vertex, using the opposite group size as its increment.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| originalDegree | Original Degree | Required. Safe integer; minimum 0. |
| originalOrder | Original Order | Required. Safe integer; minimum 1. |
| isolatedGroupSize | Isolated Group Size | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| originalVertexDegree | Original Vertex Degree | Required. Safe integer. |
| addedVertexDegree | Added Vertex Degree | Required. Safe integer. |
{
"input": {
"originalDegree": 2,
"originalOrder": 5,
"isolatedGroupSize": 3
},
"output": {
"originalVertexDegree": 5,
"addedVertexDegree": 5
}
}Limitations and assumptions
- Added vertices are assumed mutually isolated before joining and each connects to every original vertex; actual disjoint graphs, degrees, and edges are not inspected.
- 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
- Edge Endpoint Degree Product
Require nonnegative integer firstDegree and secondDegree and return their exact product as productDecimal.
- Graph Cartesian Product Degree Term
Require nonnegative integer firstDegree and secondDegree and return their sum.