{"id":"W4406171630","doi":"10.61091/um121-09","title":"Radio Number of Cartesian Products of Complete Bipartite Graphs and Odd Cycles","year":2024,"lang":"en","type":"article","venue":"Utilitas Mathematica","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Qinghai Normal University; Natural Science Foundation of Qinghai; National Natural Science Foundation of China","keywords":"Mathematics; Cartesian product; Bipartite graph; Combinatorics; Complete bipartite graph; Discrete mathematics; Graph","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":[],"consensus_categories":[],"category_scores_codex":[0.0005899411,0.0002195351,0.0005551564,0.0001408807,0.00007561417,0.0000232412,0.0002049896,0.00008360636,0.0002570041],"category_scores_gemma":[0.0004333661,0.0001625538,0.0001469206,0.0003221163,0.00050916,0.00009673968,0.0001198411,0.0001351814,0.000009486942],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000009144965,"about_ca_system_score_gemma":0.00002751843,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006080806,"about_ca_topic_score_gemma":0.000001726581,"domain_scores_codex":[0.9984401,0.0000871435,0.0006284596,0.0003019918,0.0002994467,0.0002428525],"domain_scores_gemma":[0.9982226,0.0008618852,0.0001366904,0.0006131937,0.00009288115,0.00007270032],"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":[0.00001391983,0.00007385673,0.0003401094,0.005118852,0.000182127,0.000005858028,0.005758372,1.40196e-7,0.001629743,0.9845135,0.001545073,0.0008184603],"study_design_scores_gemma":[0.0001480499,0.00004333199,0.0005827245,0.0005454817,0.0001694583,0.00007663792,0.0003808238,0.0004038685,0.003960029,0.9928104,0.0007190213,0.0001601276],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9836398,0.001921014,0.0003244527,0.000188271,0.000206477,0.0004512749,0.0001200276,0.0001429081,0.01300575],"genre_scores_gemma":[0.9752628,0.00004780927,0.02436448,0.00001012999,0.00002744177,0.00001384991,0.000003216623,0.00003938297,0.0002308479],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02404002,"threshold_uncertainty_score":0.662875,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03965243051451393,"score_gpt":0.3146020168826811,"score_spread":0.2749495863681671,"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."}}