Super point graph and point completion number
Bibliographic record
Abstract
Graph invariants, often regarded as topological indices, play a pivotal role in understanding and quantifying the structural properties of graphs. Among these, the line completion number has emerged as a significant measure of a graph’s edge connectivity and topology. In 1992, Bagga et al. defined a generalization of line graphs, namely super line graphs, and introduced the concept of the line completion number as a topological index of a graph. They calculated the line completion number for several classes of graphs, showcasing its utility in understanding graph structure. The line completion number of a graph, is the smallest index such that the super line graph becomes a complete graph. This index encapsulates the interplay between edge relationships and structural complexity, making it a versatile tool for characterizing graphs. Building upon this foundation, we analogously introduce the concepts of super point graphs and the point completion number, as vertex-centric topological indices. We establish a relationship between the point completion number and the line completion number, further extending the framework of graph invariants. Additionally, we compute the point completion numbers for various graph classes and analyze their structural implications. Our findings emphasize the significance of completion numbers as robust descriptors for graph topology, with potential applications in network analysis, chemistry, and other domains.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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".