{"paper":{"title":"Merging the A- and Q-spectral theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"V. Nikiforov","submitted_at":"2016-07-11T16:14:56Z","abstract_excerpt":"Let $G$ be a graph with adjacency matrix $A\\left( G\\right) $, and let $D\\left( G\\right) $ be the diagonal matrix of the degrees of $G.$ The signless Laplacian $Q\\left( G\\right) $ of $G$ is defined as $Q\\left( G\\right) :=A\\left( G\\right) +D\\left( G\\right) $.\n  Cvetkovi\\'{c} called the study of the adjacency matrix the $A$% \\textit{-spectral theory}, and the study of the signless Laplacian--the $Q$\\textit{-spectral theory}. During the years many similarities and differences between these two theories have been established. To track the gradual change of $A\\left( G\\right) $ into $Q\\left( G\\right)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03015","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}