{"paper":{"title":"Center, centroid and subtree core of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dheer Noal Sunil Desai, Kamal Lochan Patra","submitted_at":"2016-12-08T13:45:54Z","abstract_excerpt":"For $n\\geq 5$ and $2\\leq g\\leq n-3,$ consider the tree $P_{n-g,g}$ on $n$ vertices which is obtained by adding $g$ pendant vertices to one degree $1$ vertex of the path $P_{n-g}$. We call the trees $P_{n-g,g}$ as path-star trees. We prove that over all trees on $n\\geq 5$ vertices, the distance between center and subtree core and the distance between centroid and subtree core are maximized by some path-star trees. We also prove that the tree $P_{n-g_0,g_0}$ maximizes both the distances among all path-star trees on $n$ vertices, where $g_0$ is the smallest positive integer such that $2^{g_0}+g_0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02642","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"}