{"id":"W4415525816","doi":"10.61091/jcmcc128-03","title":"Preservers of strong vertex labeling numbers of graphs","year":2025,"lang":"","type":"article","venue":"Journal of Combinatorial Mathematics and Combinatorial Computing","topic":"Graph Labeling and Dimension Problems","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Vertex (graph theory); Chromatic scale; Graph; Undirected graph; Operator (biology); Set (abstract data type)","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":[0.001710807,0.000826777,0.0004609594,0.001924312,0.001649912,0.003488402,0.0009905895,0.0007290221,0.008214851],"category_scores_gemma":[0.005123576,0.0005891554,0.001000155,0.001327302,0.003152522,0.004062246,0.002418347,0.002325204,0.001009906],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001839608,"about_ca_system_score_gemma":0.000753982,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006059267,"about_ca_topic_score_gemma":0.0008071335,"domain_scores_codex":[0.997622,0.0005229168,0.0001433775,0.0006967432,0.0006107538,0.0004041162],"domain_scores_gemma":[0.9944061,0.002330351,0.0009755115,0.0007566142,0.0007225614,0.0008088932],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.0001630152,0.00006600338,0.0006318032,0.00005977581,0.00001504201,0.0001051441,0.0003382254,0.003575427,0.004316478,0.9679902,0.001894816,0.02084414],"study_design_scores_gemma":[0.00005509555,0.000243759,0.001148806,0.00002915596,0.00002618932,0.0003692612,0.000218647,0.0267101,0.009632663,0.951367,0.01015305,0.00004629098],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5799402,0.0003852222,0.2991312,0.00111543,0.0004849559,0.000144425,0.0009405653,0.001252429,0.1166056],"genre_scores_gemma":[0.9251708,0.000234956,0.04359291,0.0002933347,0.0003360576,0.0002554537,0.0006274287,0.0003424185,0.02914661],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008214851,"threshold_uncertainty_score":0.02748144,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01417680864429658,"score_gpt":0.2592842111561585,"score_spread":0.2451074025118619,"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."}}