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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)
A construction is given for an infinite family { n } of finite vertex-transitive non-Cayley graphs of fixed valency with the property that the order of the vertex-stabilizer in the smallest vertex-transitive group of automorphisms of n is a strictly increasing function of n. For each n the graph is 4-valent and arc-transitive, with automorphism group a(More)