{"id":"W7083585982","doi":"10.61091/um124-04","title":"\\(k\\)-domination and \\(k\\)-tuple total domination for some chessboard graphs","year":2025,"lang":"en","type":"article","venue":"Utilitas Mathematica","topic":"Geodetic Measurements and Engineering Structures","field":"Engineering","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Square (algebra); Dimension (graph theory); Domination analysis; Graph; Metric dimension","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":[0.0002083784,0.0001474821,0.0001884786,0.000134948,0.00006189555,0.00003996013,0.00007047883,0.00005849115,0.00002971081],"category_scores_gemma":[0.0001334606,0.0001378525,0.00005221866,0.00009698662,0.00002877379,0.00009834141,0.00001658077,0.00006035631,0.000003734557],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003283338,"about_ca_system_score_gemma":0.000007089119,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001601214,"about_ca_topic_score_gemma":9.26515e-7,"domain_scores_codex":[0.9993235,0.000006727207,0.0002211827,0.0001430639,0.0001154456,0.0001900655],"domain_scores_gemma":[0.9996452,0.0000883235,0.00001860443,0.0001712211,0.0000378303,0.00003886466],"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":[0.00004023816,0.00009587654,0.00008121651,0.006419199,0.0004088414,0.00000155324,0.001835227,0.004661125,0.02311555,0.8662679,0.01106012,0.08601319],"study_design_scores_gemma":[0.001861294,0.00006311473,0.009957572,0.0003386819,0.000199346,0.00001008266,0.0003666961,0.4620449,0.01764047,0.5032647,0.003732076,0.0005209871],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8496589,0.001732327,0.1362657,0.0003735393,0.001012544,0.001253883,0.0000440048,0.0005629386,0.009096211],"genre_scores_gemma":[0.9897701,0.0000166128,0.009707761,0.00001833519,0.00002415359,0.0001156525,0.00001087544,0.00001902915,0.0003174884],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4573838,"threshold_uncertainty_score":0.5621464,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007561251675427035,"score_gpt":0.2206023824529386,"score_spread":0.2130411307775116,"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."}}