{"id":"W2062017656","doi":"10.1002/jgt.20102","title":"On graphs whose Laplacian matrices have distinct integer eigenvalues","year":2005,"lang":"en","type":"article","venue":"Journal of Graph Theory","topic":"Graph theory and applications","field":"Mathematics","cited_by":20,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Regina","funders":"","keywords":"Laplacian matrix; Mathematics; Combinatorics; Eigenvalues and eigenvectors; Conjecture; Laplace operator; Resistance distance; Algebraic connectivity; Graph; Discrete mathematics; Integer (computer science); Spectral graph theory; Matrix (chemical analysis); Line graph; Graph power; Mathematical analysis; Computer science; Physics","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":[0.002165816,0.0002358086,0.0003813461,0.0005565459,0.0002322592,0.00005913577,0.0004905044,0.0001065708,0.0003655882],"category_scores_gemma":[0.0004294752,0.0001719788,0.0004991213,0.0003379367,0.0002192438,0.0002418099,0.00003512451,0.000480281,0.00005787308],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003351433,"about_ca_system_score_gemma":0.0000313042,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":8.500498e-7,"about_ca_topic_score_gemma":0.000009376056,"domain_scores_codex":[0.9981605,0.0003303097,0.0006995694,0.0001708048,0.0003700273,0.0002688272],"domain_scores_gemma":[0.9971018,0.00146687,0.0006963515,0.0003875749,0.0001786025,0.000168816],"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":[0.0002706145,0.0004203965,0.0004194955,0.00002460974,0.0001438281,0.00001302469,0.0007929889,0.00001330304,0.0002653919,0.9875217,0.004843303,0.005271314],"study_design_scores_gemma":[0.0004611087,0.0001994206,0.0006649034,0.0001343509,0.0001505717,0.00008784581,0.0006424566,0.000009851013,0.001685876,0.9917911,0.003980233,0.0001923014],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9799148,0.0007503701,0.004347352,0.0006134512,0.0002067091,0.0001940714,0.00002107828,0.00006142294,0.01389069],"genre_scores_gemma":[0.9957781,0.0001162047,0.002902902,0.0002890262,0.0002252121,0.000009243113,0.000001514586,0.0000364692,0.0006412934],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01586328,"threshold_uncertainty_score":0.7013091,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02432364321713661,"score_gpt":0.3075562901536715,"score_spread":0.2832326469365349,"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."}}