Title: A classification of nilpotent $3$-BCI groups
Abstract: Given a finite group G and a subset S ⊆ G, the bi-Cayley graph BCay(G,S) is the graph whose vertex set is G × {0,1} and edge set is {{(x,0),(sx,1)} : x ∈ G,s ∈ S}. A bi-Cayley graph BCay(G,S) is called a BCI-graph if for any bi