{"id":"W2137496495","doi":"10.1016/j.laa.2010.02.002","title":"On the normalized Laplacian energy and general Randić index <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si1.gif\" overflow=\"scroll\"><mml:mrow><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mo>-</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> of graphs","year":2010,"lang":"lv","type":"article","venue":"Linear Algebra and its Applications","topic":"Graph theory and applications","field":"Mathematics","cited_by":120,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Regina","funders":"","keywords":"Adjacency matrix; Combinatorics; Energy (signal processing); Laplacian matrix; Upper and lower bounds; Laplace operator; Mathematics; Edit distance; Algorithm; Eigenvalues and eigenvectors; Discrete mathematics; Graph; Physics; Statistics; 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":["metaepi_narrow","sts","scholarly_communication","research_integrity","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.002036999,0.0009249045,0.0004134406,0.0006063473,0.00244957,0.001114988,0.002143396,0.002346403,0.3665301],"category_scores_gemma":[0.001109839,0.001601034,0.001563133,0.001598678,0.002146285,0.001020353,0.001458025,0.00180669,0.001027837],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000008336499,"about_ca_system_score_gemma":0.0009621494,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0009994215,"about_ca_topic_score_gemma":0.001719849,"domain_scores_codex":[0.9918491,0.0004621437,0.002013977,0.001784572,0.001890662,0.001999584],"domain_scores_gemma":[0.991246,0.002488149,0.002138589,0.002729347,0.0002571532,0.001140798],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"bench_or_experimental","study_design_scores_codex":[0.0009246072,0.0004692604,0.00001334123,0.0007558052,0.001258208,0.0001060896,0.001635015,0.0002850262,0.007047366,0.7994109,0.1864462,0.001648161],"study_design_scores_gemma":[0.002522831,0.0009718343,0.0001174354,0.0005870775,0.001754611,0.0007164342,0.001397136,0.03531241,0.9397447,0.003932878,0.0113935,0.001549226],"study_design_candidate":"bench_or_experimental","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5783156,0.001108966,0.001590359,0.001025043,0.0008758712,0.00009133579,0.0006073209,0.0002048867,0.4161806],"genre_scores_gemma":[0.9857825,0.002141213,0.002492472,0.002047777,0.001649758,0.003237366,0.001275846,0.0006836473,0.0006894149],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.9326972,"threshold_uncertainty_score":0.999922,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01442548016866956,"score_gpt":0.2381827723223012,"score_spread":0.2237572921536317,"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."}}