Topics in Edge Regular Graphs

Abstract

A graph, G, is edge-regular with parameters (n,d,lambda) if G is regular of degree d on n vertices and for all u, v in V(G) such that uv is in E(G), the order of the intersection of N(u) and N(v) is lambda, where N(v) denotes the open neighborhood of a vertex v in V(G). We explore the structure of edge-regular graphs with particular emphasis on the case lambda=1.