{"paper":{"title":"Edge-bipancyclicity of bubble-sort star graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jia Guo, Mei Lu","submitted_at":"2019-07-15T09:10:49Z","abstract_excerpt":"The interconnection network considered in this paper is the bubble-sort star graph. The $n$-dimensional bubble-sort star graph $BS_n$ is a bipartite and $(2n-3)$-regular graph of order $n!$. A bipartite graph $G$ is edge-bipancyclic if each edge of $G$ lies on a cycle of all even length $l$ with $4\\leq l\\leq |V(G)|$. In this paper, we show that the $n$-dimensional bubble-sort star graph $BS_n$ is edge-bipancyclic for $n\\ge 3$ and for each even length $l$ with $4\\leq l\\leq n!$, every edge of $BS_n$ lies on at least four different cycles of length $l$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06378","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"}