{"paper":{"title":"A spectral bound for graph irregularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Felix Goldberg","submitted_at":"2013-08-18T15:07:13Z","abstract_excerpt":"The imbalance of an edge $e=\\{u,v\\}$ in a graph is defined as $i(e)=|d(u)-d(v)|$, where $d(\\cdot)$ is the vertex degree. The irregularity $I(G)$ of $G$ is then defined as the sum of imbalances over all edges of $G$. This concept was introduced by Albertson who proved that $I(G) \\leq \\frac{n^{3}}{27}$ (where $n=|V(G)|$) and obtained stronger bounds for bipartite and triangle-free graphs. Since then a number of additional bounds were given by various authors. In this paper we prove a new upper bound, which improves a bound found by Zhou and Luo in 2011. Our bound involves the Laplacian spectral "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3867","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"}