Strongly regular graph

Definition

Definition for finite graphs

Suppose $G$ is a finite undirected graph with $n$ vertices. Suppose $d,\lambda ,\mu$ are nonnegative integers. We say that $G$ is a strongly regular graph of type $(n,d,\lambda ,\mu )$ (we sometimes write this as ${\mbox{srg}}(n,d,\lambda ,\mu )$) if it satisfies all of the following conditions:

1. $G$ is a $d$-regular graph, i.e., the degree of every vertex of $G$ equals $G$.
2. Any two adjacent vertices of $G$ have precisely $\lambda$ vertices that are adjacent to both of them.
3. Any two non-adjacent vertices of $G$ have precisely $\mu$ vertices that are adjacent to both of them.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
complete graph
empty graph