{"paper":{"title":"Hitting Times, Cover Cost, and the Wiener Index of a Tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Agelos Georgakopoulos, Stephan Wagner","submitted_at":"2013-02-13T20:40:57Z","abstract_excerpt":"We exhibit a close connection between hitting times of the simple random walk on a graph, the Wiener index, and related graph invariants. In the case of trees we obtain a simple identity relating hitting times to the Wiener index.\n  It is well known that the vertices of any graph can be put in a linear preorder so that vertices appearing earlier in the preorder are \"easier to reach\" by a random walk, but \"more difficult to get out of\". We define various other natural preorders and study their relationships. These preorders coincide when the graph is a tree, but not necessarily otherwise.\n  Our"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3212","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"}