{"id":"W2043963103","doi":"10.1016/j.disc.2004.12.010","title":"Completion of Laplacian integral graphs via edge addition","year":2005,"lang":"en","type":"article","venue":"Discrete Mathematics","topic":"Graph theory and applications","field":"Mathematics","cited_by":24,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Regina","funders":"","keywords":"Integrally closed; Mathematics; Combinatorics; Laplacian matrix; Algebraic connectivity; Resistance distance; Discrete mathematics; Integral graph; Laplace operator; Graph; Line graph; Graph power; Mathematical analysis","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003636095,0.0001828635,0.0003216294,0.0001275392,0.0001154367,0.00001906285,0.0002357213,0.00008922057,0.0003904708],"category_scores_gemma":[0.0001210498,0.0001580953,0.000186712,0.0002681862,0.0001538825,0.000130128,0.000042674,0.0001446103,0.00008325446],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002417911,"about_ca_system_score_gemma":0.00001103666,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002633402,"about_ca_topic_score_gemma":0.00001722498,"domain_scores_codex":[0.9988002,0.00005017219,0.0005363993,0.0001692933,0.0002395337,0.0002043701],"domain_scores_gemma":[0.9987507,0.0002961777,0.0003105082,0.0004708771,0.0001009719,0.00007071171],"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":[0.000007310928,0.0002599317,0.00003240457,0.0001691115,0.00003269092,2.972021e-7,0.001283261,0.000003800729,0.002611395,0.9920799,0.001995425,0.001524449],"study_design_scores_gemma":[0.000261869,0.00004194779,0.0001138573,0.000113892,0.00008019886,0.0000125736,0.0005563184,0.002413475,0.007569809,0.9864716,0.002178093,0.0001863585],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7525141,0.00004820558,0.2114456,0.0006274105,0.0000987994,0.0008783054,0.0002244775,0.0003073023,0.03385577],"genre_scores_gemma":[0.9125691,0.000006940641,0.08687901,0.00004568063,0.00006108793,0.00006268993,0.00007781477,0.00003151016,0.0002661594],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.160055,"threshold_uncertainty_score":0.6446937,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03295297523356717,"score_gpt":0.3015378562735073,"score_spread":0.2685848810399402,"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."}}