{"paper":{"title":"On spectral spread of generalized distance matrix of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Alhevaz, Hilal A. Ganie, M. Baghipur, S. Pirzada","submitted_at":"2019-07-22T17:55:42Z","abstract_excerpt":"For a simple connected graph $G$, let $D(G)$, $Tr(G)$, $D^{L}(G)$ and $D^{Q}(G)$, respectively be the distance matrix, the diagonal matrix of the vertex transmissions, distance Laplacian matrix and the distance signless Laplacian matrix of a graph $G$. The convex linear combinations $D_{\\alpha}(G)$ of $Tr(G)$ and $D(G)$ is defined as $D_{\\alpha}(G)=\\alpha Tr(G)+(1-\\alpha)D(G)$, $0\\leq \\alpha\\leq 1$. As $D_{0}(G)=D(G), ~~~ 2D_{\\frac{1}{2}}(G)=D^{Q}(G), ~~~ D_{1}(G)=Tr(G)$ and $D_{\\alpha}(G)-D_{\\beta}(G)=(\\alpha-\\beta)D^{L}(G)$, this matrix reduces to merging the distance spectral, distance Lapl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09462","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"}