Moore graphs and beyond: A survey of the degree/diameter problem Page 1 Moore graphs
and beyond: A survey of the degree/diameter problem Mirka Miller School of Mathematical …

The degree/diameter problem for mixed graphs asks for the largest possible order of a
mixed graph with given diameter and degree parameters. Similarly the degree/geodecity …

The undirected degree/diameter and degree/girth problems and their directed analogues
have been studied for many decades in the search for efficient network topologies. Recently …

A digraph in which, for every pair of vertices u and v (not necessarily distinct), there is at
most one walk of length≤ k from u to v is called a k-geodetic digraph. The order N (d, k) of a …

An almost Moore digraph is a diregular digraph of degree $ d> 1$, diameter $ k> 1$ and
order $ d+ d^ 2+\cdots+ d^ k $. Their existence has only been shown for $ k= 2$. It has also …

The Degree/diameter problem asks for the largest graphs given diameter and maximum
degree. This problem has been extensively studied both for directed and undirected graphs …

An almost Moore (d, k)-digraph is a regular digraph of degree d> 1, diameter k> 1 and order
N (d, k)= d+ d2+⋯+ dk. So far, their existence has only been shown for k= 2, whilst it is …

Digraphs of maximum out-degree at most d> 1, diameter at most k> 1 and order N (d, k)=
d+⋯+ dk are called almost Moore or (d, k)-digraphs. So far, the problem of their existence …

A k-geodetic digraph with minimum out-degree d has excess ϵ if it has order M (d, k)+ ϵ,
where M (d, k) represents the Moore bound for out-degree d and diameter k. For given ϵ, it …

The degree/diameter problem for directed graphs is the problem of determining the largest
possible order for a digraph with given maximum out-degree d and diameter k. An upper …