Characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic flower vase graph
Bibliographic record
Abstract
Abstract This research discussed the characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic flower vase graph. The entries of the antiadjacency matrix of a directed graph represent the presence or the absence of a directed arc from one vertex to the others. If A is the adjacency matrix of a graph <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block" overflow="scroll"> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>→</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> , then the antiadjacency matrix B of graph <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block" overflow="scroll"> <mml:mrow> <mml:mover accent="true"> <mml:mrow> <mml:mi>G</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>→</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> is B = J − A , where J is the square matrix with all entries equal to one. The general form of characteristic polynomial coefficients of the antiadjacency matrix of directed unicyclic flower vase graph can be obtained by calculating the sum of determinants of the antiadjacency matrices of all induced cyclic and acyclic subgraphs, while the eigenvalues were obtained by using polynomial factorization and Horner’s method. This paper gives the characteristic polynomial coefficients and eigenvalues of antiadjacency matrix of directed unicyclic flower vase graph. The characteristic polynomial can be considered as a function that depends on the number of vertices.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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".