{"id":"W1988315105","doi":"10.5539/jmr.v3n1p66","title":"Some Results on Prime and k-Prime Labeling","year":2011,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Graph Labeling and Dimension Problems","field":"Computer Science","cited_by":17,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Combinatorics; Prime (order theory); Graph labeling; Graph; Edge-graceful labeling; Prime number; Discrete mathematics; Graph power; Line 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001414304,0.0007480473,0.0008315302,0.002058089,0.002056989,0.002512951,0.001008722,0.001262009,0.008017628],"category_scores_gemma":[0.005105994,0.0005919196,0.001040885,0.003630245,0.003208354,0.006297369,0.001900831,0.002393994,0.001084161],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001634195,"about_ca_system_score_gemma":0.000654284,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008750586,"about_ca_topic_score_gemma":0.0005244931,"domain_scores_codex":[0.9990294,0.0002102326,0.00005824041,0.0003086184,0.0001974548,0.0001960129],"domain_scores_gemma":[0.995368,0.003114098,0.0004588518,0.0004450836,0.0003064967,0.0003074803],"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":[0.00008186575,0.00004281589,0.001238065,0.0002404398,0.00001563808,0.0001912897,0.0004415145,0.00381126,0.001447757,0.9672094,0.004669319,0.02061075],"study_design_scores_gemma":[0.00001417652,0.00004139484,0.0007479033,0.00004190117,0.00002522388,0.0004323223,0.0001755449,0.006130511,0.001017098,0.974529,0.0168239,0.00002113226],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3138421,0.01345048,0.3947947,0.007877923,0.0009978627,0.0001424197,0.001647478,0.0007294496,0.2665175],"genre_scores_gemma":[0.8839881,0.01025261,0.08151677,0.001800309,0.001717517,0.0001859909,0.001267452,0.0002494626,0.01902191],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.008017628,"threshold_uncertainty_score":0.02682161,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1979606587736409,"score_gpt":0.3612184441609494,"score_spread":0.1632577853873085,"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."}}