Large Cayley graphs and vertex-transitive non-Cayley graphs of given degree and diameter

Macbeth, Heather; Šiagiová, Jana; Širáň, Jozef and Vetrík, Tomáš (2010). Large Cayley graphs and vertex-transitive non-Cayley graphs of given degree and diameter. Journal of Graph Theory, 64(2) pp. 87–98.

DOI: https://doi.org/10.1002/jgt.20439

Abstract

For any d≥5 and k≥3 we construct a family of Cayley graphs of degree d, diameter k, and order at least k((d-3)/3)k. By comparison with other available results in this area we show that our family gives the largest currently known Cayley graphs for a wide range of sufficiently large degrees and diameters.

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