Exoo, Geoffrey; Jajcay, Robert Dynamic cage survey. (English) Zbl 1169.05336 Electron. J. Comb. DS16, Dynamic Survey, 48 p. (2008). Summary: A \((k, g)\)-cage is a \(k\)-regular graph of girth g of minimum order. In this survey, we present the results of over 50 years of searches for cages. We present the important theorems, list all the known cages, compile tables of current record holders, and describe in some detail most of the relevant constructions.Version 2 published: May 8, 2011 (54 pages)Version 3 published: July 26, 2013 (55 pages) Cited in 72 Documents MSC: 05C35 Extremal problems in graph theory 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05-02 Research exposition (monographs, survey articles) pertaining to combinatorics Software:nauty PDFBibTeX XMLCite \textit{G. Exoo} and \textit{R. Jajcay}, Electron. J. Comb. DS16, 48 p. (2008; Zbl 1169.05336) Full Text: EuDML EMIS Online Encyclopedia of Integer Sequences: Smallest number of vertices in trivalent graph with girth (shortest cycle) = n. Order of (4,n) cage, i.e., minimal order of 4-regular graph of girth n. Number of nonisomorphic (3,n) cage graphs. Table T(n,k) = order of (n,k)-cage (smallest n-regular graph of girth k), n >= 2, k >= 3, read by antidiagonals. Order of smallest n-regular graph of girth 5. Square array M(k,g), read by antidiagonals, of the Moore lower bound on the order of a (k,g)-cage. Order of (5,n) cage, i.e., minimal order of 5-regular graph of girth n. Order of (6,n) cage, i.e., minimal order of 6-regular graph of girth n. Order of (7,n) cage, i.e., minimal order of 7-regular graph of girth n.