{"paper":{"title":"$\\ell$-distance-balanced graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Primoz Sparl, Stefko Miklavic","submitted_at":"2017-02-17T08:52:27Z","abstract_excerpt":"Let $\\ell$ denote a positive integer. A connected graph $\\G$ of diameter at least $\\ell$ is said to be $\\ell${\\it -distance-balanced} whenever for any pair of vertices $u,v$ of $\\G$ such that $d(u,v)=\\ell$, the number of vertices closer to $u$ than to $v$ is equal to the number of vertices closer to $v$ than to $u$. In this paper we present some basic properties of $\\ell$-distance-balanced graphs and study in more detail $\\ell$-distance-balanced graphs of diameter at most $3$. We also investigate the $\\ell$-distance-balanced property of some well known families of graphs such as the generalize"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05257","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"}