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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.

The main topic of the paper is the question of the existence of self-complementary Cayley graphs Cay(G; S) with the property S 6 = G # n S for all 2 Aut(G). We answer this question in the positive by constructing an innnite family of self-complementary circulants with this property. Moreover, we obtain a complete classiication of primes p for which there… (More)

It is well-known that any nite simple graph ? is an induced sub-graph of some exponentially larger strongly regular graph ? (e.g. 2, 8]). No general polynomial-size construction has been known. For a given-nite simple graph ? on v vertices we present a construction of a strongly regular graph ? on O(v 4) vertices that contains ? as its induced sub-graph. A… (More)