{"id":"W54538453","doi":"","title":"The Basis Number of the Direct Product of a Theta Graph and a Path.","year":2005,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Graph Labeling and Dimension Problems","field":"Computer Science","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Direct product; Graph; Combinatorics; Path (computing); Basis (linear algebra); Product (mathematics); Discrete mathematics; Computer science; Geometry","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0006556479,0.0004928384,0.0006926807,0.001931386,0.002133956,0.00383488,0.001100023,0.001189974,0.01787338],"category_scores_gemma":[0.002851143,0.0003982987,0.0005792798,0.001310496,0.002265676,0.004524175,0.001698655,0.00208316,0.004004228],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001128873,"about_ca_system_score_gemma":0.0008003917,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001146974,"about_ca_topic_score_gemma":0.001420582,"domain_scores_codex":[0.9993371,0.0001700322,0.00003245721,0.0001541872,0.0001113392,0.0001948546],"domain_scores_gemma":[0.9982342,0.0007900252,0.0001998297,0.0002464955,0.0002198951,0.0003095942],"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":[0.0001749289,0.00003095412,0.0009561859,0.00008770255,0.0000123094,0.00005525336,0.0001777816,0.001146204,0.002614997,0.9714588,0.007320517,0.01596447],"study_design_scores_gemma":[0.00002416259,0.0000380053,0.0009969809,0.00004651238,0.00002137886,0.0002799631,0.0002577147,0.005241499,0.003577862,0.9731976,0.01629149,0.00002680876],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.601651,0.001488387,0.1217581,0.003907292,0.001072381,0.00008667781,0.003681204,0.0007633684,0.2655915],"genre_scores_gemma":[0.9283502,0.0007256526,0.03250001,0.0003291068,0.0002532563,0.0001098032,0.001431214,0.0003014395,0.03599945],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01787338,"threshold_uncertainty_score":0.0597924,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007262431607025712,"score_gpt":0.2159267809290735,"score_spread":0.2086643493220478,"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."}}