Cayley cages

Exoo, Geoffrey; Jajcay, Robert and Širáň, Jozef (2013). Cayley cages. Journal of Algebraic Combinatorics, 38(1) pp. 209–224.



A (k, g)-Cayley cage is a k-regular Cayley graph of girth g and smallest possible order. We present an explicit construction of (k, g)-Cayley graphs for all parameters k ≥ 2 and g ≥ 3 and generalize this construction to show that many wellknown small k-regular graphs of girth g can be constructed in this way. We also establish connections between this construction and topological graph theory, and ddress the question of the order of (k, g)-Cayley cages.

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