{"paper":{"title":"The energy change of the complete multipartite graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chang-Xiang He, Hai-Ying Shan, Zhen-Sheng Yu","submitted_at":"2017-11-11T08:15:21Z","abstract_excerpt":"The energy of a graph is defined as the sum of the absolute values of all eigenvalues of the graph. Akbari et al. \\cite{S. Akbari} proved that for a complete multipartite graph $K_{t_1 ,\\ldots,t_k}$, if $t_i\\geq 2 \\ (i=1,\\ldots,k)$, then deleting any edge will increase the energy. A natural question is how the energy changes when $\\min\\{t_1 ,\\ldots,t_k\\}=1$. In this paper, we will answer this question and completely determine how the energy of a complete multipartite graph changes when one edge is removed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04095","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"}