{"paper":{"title":"Laplacian spectral characterization of some graph products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Suijie Wang, Xiaogang Liu","submitted_at":"2010-07-15T04:15:51Z","abstract_excerpt":"This paper studies the Laplacian spectral characterization of some graph products. We consider a class of connected graphs: $\\mathscr{G}={G : |EG|\\leq|VG|+1}$, and characterize all graphs $G\\in\\mathscr{G}$ such that the products $G\\times K_m$ are $L$-DS graphs. The main result of this paper states that, if $G\\in\\mathscr{G}$, except for $C_{6}$ and $\\Theta_{3,2,5}$, is $L$-DS graph, so is the product $G\\times K_{m}$. In addition, the $L$-cospectral graphs with $C_{6}\\times K_{m}$ and $\\Theta_{3,2,5}\\times K_{m}$ have been found."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2472","kind":"arxiv","version":3},"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"}