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Record W173255084

On strongly regular graphs

2009· dissertation· en· W173255084 on OpenAlex
Majid Behbahani

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueSpectrum Research Repository (Concordia University) · 2009
Typedissertation
Languageen
FieldMathematics
TopicFinite Group Theory Research
Canadian institutionsConcordia University
Fundersnot available
KeywordsMathematicsTwo-graphStrongly regular graphAutomorphismCombinatoricsAdjacency matrixIndifference graphSymmetric graphDiscrete mathematicsRegular graphUpper and lower boundsGraph automorphismChordal graphPathwidthGraphLine graphVoltage graphGraph power
DOInot available

Abstract

fetched live from OpenAlex

Strongly regular graphs are regular graphs with the additional property that the number of common neighbours for two vertices depends only on whether the vertices are adjacent or non-adjacent. From an algebraic point of view, a graph is strongly regular if its adjacency matrix has exactly three eigenvalues. Strongly regular graphs have very interesting algebraic properties due to their strong regularity conditions. Many strongly regular graphs are known to have large and interesting automorphism groups [23]. In [23] it is also conjectured that almost all strongly regular graphs are asymmetric. Peter Cameron in [7] mentions that "Strongly regular graphs lie on the cusp between highly structured and unstructured." Although strongly regular graphs have been studied extensively since they were introduced, there is very little known about the automorphism group of an arbitrary strongly regular graph based on its parameters. In this thesis, we have developed theory for studying the automorphisms of strongly regular graphs. Our study is both mathematical and computational. On the computational side, we introduce the notion of orbit matrices. Using these matrices, we were able to show that some strongly regular graphs do not admit an automorphism of a certain order. Given the size of the automorphism, we can generate all of the orbit matrices, using a computer program. Another computer program is implemented that generates all the strongly regular graphs from that orbit matrix. From a mathematical point of view, we have found an upper bound on the number of fixed points of the automorphisms of a strongly regular graph. This upper bound is a new upper bound and is obtained by algebraic techniques

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Science and technology studies, Research integrity
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.106
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.001
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0040.003
Science and technology studies0.0010.000
Scholarly communication0.0000.000
Open science0.0020.000
Research integrity0.0010.004
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.044
GPT teacher head0.320
Teacher spread0.276 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it