{"paper":{"title":"Extremal problems for the p-spectral radius of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Liying Kang, Vladimir Nikiforov","submitted_at":"2014-02-13T18:04:08Z","abstract_excerpt":"The $p$-spectral radius of a graph $G\\ $of order $n$ is defined for any real number $p\\geq1$ as \\[ \\lambda^{\\left( p\\right) }\\left( G\\right) =\\max\\left\\{ 2\\sum_{\\{i,j\\}\\in E\\left( G\\right) \\ }x_{i}x_{j}:x_{1},\\ldots,x_{n}\\in\\mathbb{R}\\text{ and }\\left\\vert x_{1}\\right\\vert ^{p}+\\cdots+\\left\\vert x_{n}\\right\\vert ^{p}=1\\right\\} . \\] The most remarkable feature of $\\lambda^{\\left( p\\right) }$ is that it seamlessly joins several other graph parameters, e.g., $\\lambda^{\\left( 1\\right) }$ is the Lagrangian, $\\lambda^{\\left( 2\\right) }$ is the spectral radius and $\\lambda^{\\left( \\infty\\right) }/2$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3239","kind":"arxiv","version":2},"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"}