{"paper":{"title":"Distance and distance signless Laplacian spread of connected graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guanglong Yu, Lihua You, Liyong Ren","submitted_at":"2016-07-02T07:32:11Z","abstract_excerpt":"For a connected graph $G$ on $n$ vertices, recall that the distance signless Laplacian matrix of $G$ is defined to be $\\mathcal{Q}(G)=Tr(G)+\\mathcal{D}(G)$, where $\\mathcal{D}(G)$ is the distance matrix, $Tr(G)=diag(D_1, D_2, \\ldots, D_n)$ and $D_{i}$ is the row sum of $\\mathcal{D}(G)$ corresponding to vertex $v_{i}$. Denote by $\\rho^{\\mathcal{D}}(G),$ $\\rho_{min}^{\\mathcal{D}}(G)$ the largest eigenvalue and the least eigenvalue of $\\mathcal{D}(G)$, respectively. And denote by $q^{\\mathcal{D}}(G)$, $q_{min}^{\\mathcal{D}}(G)$ the largest eigenvalue and the least eigenvalue of $\\mathcal{Q}(G)$, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00473","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"}