{"id":"W2037431636","doi":"10.4153/cmb-2011-107-3","title":"Characterizations of Three Classes of Zero-Divisor Graphs","year":2011,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Zero divisor; Combinatorics; Vertex (graph theory); Commutative ring; Discrete mathematics; Zero (linguistics); Graph; Commutative property","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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0002717238,0.0001872577,0.0004748102,0.0002343962,0.00006385036,0.00001225601,0.0003437781,0.0001253565,0.0109061],"category_scores_gemma":[0.0007844132,0.0001698187,0.0001550952,0.0001965525,0.0002532534,0.00003861234,0.00003718478,0.0001256735,0.0006164302],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002921917,"about_ca_system_score_gemma":0.0001436402,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007566976,"about_ca_topic_score_gemma":0.0012974,"domain_scores_codex":[0.9985542,0.00003717578,0.0006320408,0.0002051938,0.0002124773,0.0003588734],"domain_scores_gemma":[0.9985039,0.0002737988,0.0002344756,0.0005072728,0.000143939,0.0003365965],"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":[0.000006129344,0.0001913144,0.00105437,0.000505599,0.00006228576,0.000008505173,0.0008880526,8.036422e-8,0.0006251553,0.9914436,0.00484988,0.0003650236],"study_design_scores_gemma":[0.0002282589,0.00007429278,0.004752709,0.000258963,0.0000798106,0.00001172829,0.0001287803,0.00002767263,0.004512426,0.9872277,0.002466626,0.0002309955],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.938481,0.0000447352,0.009344336,0.0005561711,0.00009241507,0.0004610439,0.0001011886,0.00006061323,0.05085853],"genre_scores_gemma":[0.9820734,0.000008606455,0.01697664,0.0001094748,0.00002389294,0.00002539734,0.000007215006,0.00004458996,0.0007307313],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.0501278,"threshold_uncertainty_score":0.989998,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05728594963366447,"score_gpt":0.242465937982543,"score_spread":0.1851799883488785,"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."}}