{"paper":{"title":"A new result similar to the Graham-Pollak theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zhi-Wei Sun","submitted_at":"2023-03-22T15:10:26Z","abstract_excerpt":"Let $n>1$ be an integer, and let $T$ be a tree with $n+1$ vertices $v_1,\\ldots,v_{n+1}$, where $v_1$ and $v_{n+1}$ are two leaves of $T$. For each edge $e$ of $T$, assign a complex number $w(e)$ as its weight. We obtain that $$\\det[x+d(v_{j+1},v_k)]_{1\\le j,k\\le n}=2^{n-2}\\prod_{e\\in E(T)}w(e),$$ where $d(v_{j+1},v_k)$ is the weighted distance between $v_{j+1}$ and $v_k$ in the tree $T$. This is similar to the celebrated Graham-Pollak theorem on determinants of distance matrices for trees. Actually, a more general result is deduced in this paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.12629","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.12629/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}