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In this paper, we show that [Formula: see text] is a lexicographic product of two graphs, and using this, we show that every minimum cyclic vertex-cut of [Formula: see text] isolates a 4-cycle, and prove that the edge neighbor connectivity of [Formula: see text] is [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219265921500249","type":"journal-article","created":{"date-parts":[[2022,1,30]],"date-time":"2022-01-30T05:45:43Z","timestamp":1643521543000},"source":"Crossref","is-referenced-by-count":0,"title":["Some Properties of the Balanced Hypercube"],"prefix":"10.1142","volume":"22","author":[{"given":"Hui-Wen","family":"Cheng","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhongguancun Institute, Beijing 100083, P. R. China"}]},{"given":"Jin-Xin","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Beijing Jiaotong University, Beijing 100044, P. R. 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