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arXiv · 1511.03706

Cayley graphs of diameter two with order greater than 0.684 of the Moore bound for any degree

Marcel Abas
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Abstract

It is known that the number of vertices of a graph of diameter two cannot exceed $d^2+1$. In this contribution we give a new lower bound for orders of Cayley graphs of diameter two in the form $C(d,2)>0.684d^2$ valid for all degrees $d\geq 360756$. The result is a significant improvement of currently known results on the orders of Cayley graphs of diameter two.

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Marcel Abas. 2016-05-22. Cayley graphs of diameter two with order greater than 0.684 of the Moore bound for any degree. https://doi.org/10.1016/j.ejc.2016.04.008

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