Yuansheng, YangLiang, Weifa2015-12-132015-12-130012-365Xhttp://hdl.handle.net/1885/86697A (D;g)-cage is a graph having the minimum number of vertices, with degree set D and girth g. Denote by f(D;g) the number of vertices in a (D;g)-cage. In this paper it is shown that f({r,m};6)≥2(rm-m+1) for any 2≤r<m, and f({r,m};6)=2(rm-m+1) if eitheKeywords: Functions; Mathematical models; Set theory; Symmetric graphs; Graph theory Cage; Degree set; Girth; Symmetric graphThe minimum number of vertices with girth 6 and degree set D={r,m}200310.1016/S0012-365X(02)00758-62015-12-12