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 …

Power Graphs: A Survey Page 1 www.ejgta.org Electronic Journal of Graph Theory and
Applications 1 (2) (2013), 125–147 Power Graphs: A Survey Jemal Abawajya, Andrei …

Abstract An almost Moore (d, 2)-digraph is a regular directed graph of degree d> 1, diameter
k= 2 and order n one less than the (unattainable) Moore bound. Their enumeration is …

An almost Moore digraph G of degree d> 1, diameter k> 1 is a diregular digraph with the
number of vertices one less than the Moore bound. If G is an almost Moore digraph, then for …

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 …

Almost Moore digraphs appear in the context of the degree/diameter problem as a class of
extremal directed graphs, in the sense that their order is one less than the unattainable …

Regular digraphs of degree $ d> 1$, diameter $ k> 1$ and order $ N (d, k)= d+\cdots+ d^ k $
will be called almost Moore $(d, k) $-digraphs. So far, the problem of their existence has only …

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 …

In the quest for the largest known graphs many innovative approaches have been
suggested. In a wide spectrum, we can classify these approaches into general (those …

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 …