{"id":"W4415525854","doi":"10.61091/jcmcc128-04","title":"On star polynomials of digraphs and their applications to domination","year":2025,"lang":"","type":"article","venue":"Journal of Combinatorial Mathematics and Combinatorial Computing","topic":"Advanced Graph Theory Research","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Star (game theory); Digraph; Directed graph; Macdonald polynomials; Orthogonal polynomials; A* search algorithm; Difference polynomials","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":[0.001591907,0.001040309,0.001052212,0.003222389,0.001790821,0.00227255,0.001250571,0.00087511,0.01228057],"category_scores_gemma":[0.007770048,0.0006076918,0.00181432,0.005825953,0.002538484,0.004951595,0.002597221,0.00312708,0.001509801],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00355794,"about_ca_system_score_gemma":0.001379716,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.009055983,"about_ca_topic_score_gemma":0.008973237,"domain_scores_codex":[0.9989709,0.0002929554,0.00006589356,0.0002386028,0.0002259847,0.0002057344],"domain_scores_gemma":[0.9949908,0.003407133,0.000443147,0.0002190235,0.0005450417,0.00039497],"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":[0.00002397181,0.00002471583,0.0003221058,0.00008237108,0.00000992856,0.00008036556,0.0003109476,0.007704235,0.000363114,0.9730896,0.00220636,0.01578215],"study_design_scores_gemma":[0.00002091345,0.00002318335,0.0002358139,0.00003141538,0.00001253198,0.0001144038,0.00008312131,0.0362566,0.0002448497,0.9546408,0.008314986,0.00002149174],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08476017,0.002793669,0.8131688,0.002163087,0.0003874914,0.0001484835,0.001364909,0.000465113,0.09474837],"genre_scores_gemma":[0.7653864,0.007067893,0.1647971,0.001095836,0.001151067,0.0003843595,0.001475133,0.000457031,0.0581851],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01228057,"threshold_uncertainty_score":0.04108256,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01529881721057274,"score_gpt":0.299564200650805,"score_spread":0.2842653834402322,"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."}}