Matching Preclusion Number in Cartesian Product of Graphs and its Application to Interconnection Networks.
Bibliographic record
Abstract
The matching preclusion number of a graph G, mp(G), is the minimum number of edges whose deletion leaves a resulting graph that has neither perfect matchings nor almost perfect matchings. Besides its theoretical linkage with conditional connectivity and extremal graph theory, the matching preclusion number is a measure of robustness in interconnection networks. In this paper we develop general properties related to matchings in the Cartesian product of graphs which allow us, in a simple manner, to establish the matching preclusion number for some interconnection (product) networks, namely: hyper Petersen, folded Petersen, folded Petersen cube, hyperstar, star-cube and hypercube. We also conclude that the Cartesian product of graphs operation inherits the matching preclusion number optimality from factor graphs of even order, which reinforces the Cartesian product as a good network-synthesizing operator.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".