The order of a graph of maximum degree d and diameter 2 cannot exceed d2+ 1, the Moore
bound for diameter two. A combination of known results guarantees the existence of regular …

Polarity graphs, also known as Brown graphs, and their minor modifications are the largest
currently known graphs of diameter 2 and a given maximum degree d such that d− 1 is a …

Let CC d, k be the largest possible number of vertices in a cyclic Cayley graph of degree d
and diameter k, and let AC d, k be the largest order in an Abelian Cayley graph for given d …

The order of an Abelian Cayley graph of degree 2n and diameter 2 cannot exceed 2n2+ 2n+
1, which is the famous Abelian Cayley-Moore bound. Leung and Zhou [J. Combin. Theory …

We consider the degree-diameter problem for Cayley graphs of dihedral groups. We find
upper and lower bounds on the maximum number of vertices of such a graph with diameter …

It is well known that the number of vertices of a graph of diameter two and maximum degree
d is at most d 2+ 1. The number d 2+ 1 is the Moore bound for diameter two. Let C (d, 2) …

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 …

Let C (d, k) and AC (d, k) be the largest order of a Cayley graph and a Cayley graph based
on an abelian group, respectively, of degree d and diameter k. It is well known that C (d, k) …

Open Research Online oro.open.ac.uk Page 1 Open Research Online The Open University’s
repository of research publications and other research outputs Extremal Directed And Mixed …

The degree-diameter problem seeks to find the largest possible number of vertices in a
graph having given diameter and given maximum degree. Very often the problem is studied …