A Generalization of Brown's Construction for the Degree/Diameter Problem

Abstract

The degree/diameter problem is the problem of finding the largest possible number of vertices $n_{\Delta ,D}$ in a graph of given degree $\Delta$ and diameter $D$. We consider the problem for the case of diameter $D=2$. William G Brown gave a lower bound of the order of $(\Delta ,2)$-graph. In this paper, we give a generalization of his construction and improve the lower bounds for the case of $\Delta =306$ and $\Delta =307$. One is $(306,2)$-graph with $88723$ vertices, the other is $(307,2)$-graph with $88724$ vertices.

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