{"paper":{"title":"Bounds on the $\\alpha$-distance spectrum of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Changjiang Bu, Lizhu Sun, Yang Yang","submitted_at":"2019-08-11T12:24:58Z","abstract_excerpt":"For a simple, undirected and connected graph $G$, $D_{\\alpha}(G) = \\alpha Tr(G) + (1-\\alpha) D(G)$ is called the $\\alpha$-distance matrix of $G$, where $\\alpha\\in [0,1]$, $D(G)$ is the distance matrix of $G$, and $Tr(G)$ is the vertex transmission diagonal matrix of $G$. Recently, the $\\alpha$-distance energy of $G$ was defined based on the spectra of $D_{\\alpha}(G)$. In this paper, we define the $\\alpha$-distance Estrada index of $G$ in terms of the eigenvalues of $D_{\\alpha}(G)$. And we give some bounds on the spectral radius of $D_{\\alpha}(G)$, $\\alpha$-distance energy and $\\alpha$-distance"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03893","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.03893/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}