Bibliographic record
Abstract
An interesting property of an interconnected network (G) is the number of nodes at distance i from an arbitrary processor (u), namely the node centered surface area. This is an important property of a network due to its applications in various fields of study. In this research, we investigate on the surface area of two important interconnection networks, (n, k)-arrangement graphs and (n, k)-star graphs. Abundant works have been done to achieve a formula for the surface area of these two classes of graphs, but in general, it is not trivial to find an algorithm to compute the surface area of such graphs in polynomial time or to find an explicit formula with polynomially many terms in regards to the graph's parameters. Among these studies, the most efficient formula in terms of computational complexity is the one that Portier and Vaughan proposed which allows us to compute the surface area of a special case of (n, k)-arrangement and (n, k)-star graphs when k = n-1, in linear time which is a tremendous improvement over the naive solution with complexity order of O(n * n!). The recurrence we propose here has the linear computational complexity as well, but for a much wider family of graphs, namely A(n, k) for any arbitrary n and k in their defined range. Additionally, for (n, k)-star graphs we prove properties that can be used to achieve a simple recurrence for its surface area.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".