{"id":"W7117419254","doi":"10.61091/ars165-01","title":"Signless Laplacian spectral determinations of the starlike trees <span class=\"math inline\">\\(ST(n, d_1)\\)</span> and the double starlike trees <span class=\"math inline\">\\(H_n(p, p)\\)</span>","year":2025,"lang":"","type":"article","venue":"Ars Combinatoria","topic":"Graph theory and applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Vertex (graph theory); Graph; Degree (music); Tree (set theory); Path graph; Path (computing); Simple graph","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","sts","scholarly_communication","research_integrity"],"consensus_categories":["metaepi_narrow","sts","research_integrity"],"category_scores_codex":[0.004074021,0.002871235,0.003846219,0.00200849,0.003795692,0.00124605,0.005055164,0.001672963,0.0002527829],"category_scores_gemma":[0.001149328,0.00226,0.001938432,0.0068754,0.004531209,0.001277408,0.002166549,0.002882938,0.0001215207],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000570972,"about_ca_system_score_gemma":0.001389248,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001482833,"about_ca_topic_score_gemma":0.005034182,"domain_scores_codex":[0.9847664,0.002280787,0.004698561,0.002834185,0.002525552,0.002894544],"domain_scores_gemma":[0.9829856,0.005294986,0.003233556,0.005945238,0.001601687,0.0009389499],"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":[0.001387987,0.004121189,0.001829491,0.0008626436,0.001535557,0.00003283179,0.005617223,0.0002936693,0.007665678,0.9649354,0.01016422,0.001554081],"study_design_scores_gemma":[0.02135177,0.0009622515,0.01094154,0.001810285,0.004014125,0.00008495562,0.004013549,0.03358566,0.006345131,0.8429694,0.07099801,0.002923312],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9614164,0.00305921,0.0006177115,0.008777101,0.004076292,0.007068194,0.001915934,0.0006104765,0.01245872],"genre_scores_gemma":[0.9869023,0.003271223,0.00117029,0.0006070759,0.0002843918,0.001232854,0.0002971566,0.0004206477,0.005814089],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.121966,"threshold_uncertainty_score":0.9997907,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01417958368905303,"score_gpt":0.2587435981275346,"score_spread":0.2445640144384815,"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."}}