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 …

Abstract A $(k, g) $-cage is a $ k $-regular graph of girth $ g $ of minimum order. In this
survey, we present the results of over 50 years of searches for cages. We present the …

Strongly Regular Graphs Page 1 Chapter 9 Strongly Regular Graphs 9.1 Strongly regular
graphs A graph (simple, undirected, and loopless) of order v is called strongly regular with …

Strongly regular graphs lie at the intersection of statistical design, group theory, finite
geometry, information and coding theory, and extremal combinatorics. This monograph …

Let uj and wj be the left and right eigenvectors of P1 corresponding to the eigenvalue p1 (j)
and let their first coordinates be equal to 1. Then wj are the columns of P and mjuj are the …

Мы рассматриваем неориентированные графы без петель и кратных ребер. Для
вершины a графа Γ через Γi (a) обозначим i-окрестность вершины a, т. е. подграф …

This is a survey on some known properties of the possible Moore graph (or graphs) ϒ with
degree 57 and diameter 2. Moreover, we give some new results about it, such as the …

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 …

This survey on graphs of large girth consists of two parts. The first deals with some aspects
of algebraic and extremal graph theory loosely related to the Moore bound. Our point of …

We introduce certain paradigms for procuring computerfree explanations from data acquired
via computer algebra experimentation. Our established context is the field of algebraic …