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

Yawara Ishida

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

Combinatorics 2015-12-31 v1

Authors: Yawara Ishida

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.

Keywords

graph pebbling graph theory spectral graph theory

Cite

@article{arxiv.1512.08961,
  title  = {A Generalization of Brown's Construction for the Degree/Diameter Problem},
  author = {Yawara Ishida},
  journal= {arXiv preprint arXiv:1512.08961},
  year   = {2015}
}

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