{"id":"W1996653774","doi":"10.1016/j.ejor.2006.12.059","title":"Variable neighborhood search for extremal graphs. 16. Some conjectures related to the largest eigenvalue of a graph","year":2007,"lang":"en","type":"article","venue":"European Journal of Operational Research","topic":"Graph theory and applications","field":"Mathematics","cited_by":55,"is_retracted":false,"has_abstract":false,"ca_institutions":"Group for Research in Decision Analysis; HEC Montréal","funders":"","keywords":"Combinatorics; Mathematics; Adjacency matrix; Eigenvalues and eigenvectors; Extremal graph theory; Vertex (graph theory); Upper and lower bounds; Discrete mathematics; Graph; Chordal graph; Line graph; Voltage graph","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":[0.0243838,0.0001288137,0.0002268923,0.000515685,0.0005841313,0.00009222646,0.0007524376,0.00004146219,0.0002624534],"category_scores_gemma":[0.001795066,0.00008573545,0.0001814698,0.0009585709,0.0002123277,0.0001672196,0.0001095265,0.0006506211,0.00002672515],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00004136107,"about_ca_system_score_gemma":0.0002541099,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004327893,"about_ca_topic_score_gemma":0.000003271928,"domain_scores_codex":[0.9963825,0.001107737,0.000837842,0.00019069,0.001052844,0.0004284134],"domain_scores_gemma":[0.9946207,0.00275807,0.0001636415,0.0003403368,0.001907087,0.0002101035],"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":[0.0002737222,0.0002363619,0.0002320953,0.00002889848,0.0001030818,0.00001756099,0.0007555925,0.0004503138,0.0122551,0.9785454,0.00659947,0.0005023922],"study_design_scores_gemma":[0.001556324,0.001124881,0.00493131,0.0001517128,0.00004727472,0.0002550799,0.001095773,0.0001340929,0.01670977,0.9628754,0.0109155,0.0002028411],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8531373,0.0008266697,0.1049642,0.00559658,0.0002808434,0.001975698,0.0001464868,0.00002595633,0.0330463],"genre_scores_gemma":[0.986367,0.00002092104,0.01226268,0.0001291743,0.0002175772,0.00001062666,0.000009031095,0.00004030375,0.0009426242],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1332297,"threshold_uncertainty_score":0.8450987,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1057745998301974,"score_gpt":0.3979588401396671,"score_spread":0.2921842403094697,"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."}}