{"id":"W4402587880","doi":"10.1080/03081087.2024.2404453","title":"Bipartite unicyclic graphs with a unique perfect matching having the smallest positive eigenvalue equal to √2 − 1","year":2024,"lang":"en","type":"article","venue":"Linear and Multilinear Algebra","topic":"Graph theory and applications","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba","funders":"Council of Scientific and Industrial Research, India","keywords":"Bipartite graph; Combinatorics; Matching (statistics); Mathematics; Eigenvalues and eigenvectors; Discrete mathematics; Graph; Statistics; Physics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0005417847,0.0002376393,0.0002117727,0.0001229084,0.000373946,0.0001437158,0.0001962214,0.00007996475,0.00003782112],"category_scores_gemma":[0.0000678526,0.0001350386,0.0001006777,0.0004593971,0.0001332351,0.00008518941,0.000105202,0.0003561113,0.00005711995],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001410348,"about_ca_system_score_gemma":0.0000423314,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001386915,"about_ca_topic_score_gemma":0.0001753443,"domain_scores_codex":[0.9987645,0.0001311905,0.0002487908,0.0003954216,0.0001612793,0.0002988636],"domain_scores_gemma":[0.9985617,0.0008126898,0.00004066921,0.0003820853,0.00005679288,0.000146074],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00007557502,0.0001080497,0.0002686592,0.0001096817,0.0001878783,0.00003338326,0.009551313,0.0001210919,0.005664524,0.9768189,0.0001868418,0.006874116],"study_design_scores_gemma":[0.001479328,0.0008080713,0.002324853,0.001569144,0.0008299554,0.0003882918,0.004937378,0.0672114,0.03384564,0.8720049,0.01292268,0.001678308],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9691194,0.0002438805,0.02795307,0.0009833401,0.00006437238,0.0006962388,0.00005590425,0.000237217,0.0006466319],"genre_scores_gemma":[0.9857319,0.00003640754,0.01300102,0.0003363508,0.0001233758,0.0001036823,0.00001590737,0.00005709163,0.0005942726],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1048139,"threshold_uncertainty_score":0.5506716,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02906587094822862,"score_gpt":0.3197320274763291,"score_spread":0.2906661565281005,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}