{"id":"W2058054978","doi":"10.1016/j.laa.2009.06.011","title":"Bounds on the <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"><mml:mrow><mml:mi>Q</mml:mi></mml:mrow></mml:math>-spread of a graph","year":2009,"lang":"en","type":"article","venue":"Linear Algebra and its Applications","topic":"Graph theory and applications","field":"Mathematics","cited_by":35,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Regina","funders":"","keywords":"Adjacency matrix; Mathematics; Combinatorics; Linear algebra; Laplacian matrix; Diagonal matrix; Graph; Hermitian matrix; Eigenvalues and eigenvectors; Matrix (chemical analysis); Laplace operator; Discrete mathematics; Diagonal; Geometry; Physics; Pure mathematics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003085767,0.001871092,0.001633688,0.004790497,0.002787921,0.008996352,0.003439483,0.002168898,0.09543456],"category_scores_gemma":[0.02376976,0.0008985675,0.001892487,0.004684547,0.002703032,0.01735854,0.005870705,0.007148347,0.04311145],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003555032,"about_ca_system_score_gemma":0.001874739,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.004228281,"about_ca_topic_score_gemma":0.00465883,"domain_scores_codex":[0.9966307,0.0005802569,0.0002068837,0.0007973493,0.00122518,0.0005596194],"domain_scores_gemma":[0.9822094,0.009722746,0.0006162553,0.003130889,0.003368809,0.000951974],"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":[0.0001279149,0.00005489975,0.0004671907,0.0002380637,0.0000317352,0.00009953583,0.0004108059,0.003398849,0.001169314,0.9053876,0.05928865,0.02932539],"study_design_scores_gemma":[0.00001941547,0.00002055562,0.0005148097,0.0001346478,0.00003612271,0.0001273819,0.0001204174,0.008794867,0.001821804,0.9305245,0.05784957,0.0000359801],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.02206567,0.00438145,0.494358,0.009889393,0.001098254,0.0002037324,0.01349531,0.004876228,0.4496319],"genre_scores_gemma":[0.52064,0.009251027,0.184347,0.00466967,0.002817875,0.001412332,0.01975023,0.014617,0.242495],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.09543456,"threshold_uncertainty_score":0.3192604,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02171524323249734,"score_gpt":0.2604747639200712,"score_spread":0.2387595206875738,"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."}}