Questions tagged [strongly-regular-graph]

A strongly regular graph $G$ is a regular graph with the following additional property: there exist two integers $\lambda$ and $\mu$ such that every two adjacent vertices have $\lambda$ common neighbors and every two non-adjacent vertices have $\mu$ common neighbors.

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1answer
58 views

What is known about the non-existence of strongly regular graphs srg(n,k,0,2)?

Only two strongly regular graphs with parameters $\lambda=0$ (triangle-free) and $\mu=2$ (any two non-adjacent vertices have exactly two common neighbors) are known, see the wikipedia page: the ...
7
votes
0answers
257 views

A question related to Conways 99 graph problem

I have observed that the number of triangles $\frac{vk}{6}$ of a strongly regular graph with parameters $(v,k,1,2)$ is given by the coefficient $2(k-1)$ in the molien series of the "4-D extraspecial ...
9
votes
3answers
394 views

Generating (or availability of) large strongly regular graphs

Are there collections of already generated large strongly regular graphs available to download? By large I mean $n \geq 200$ where $n$ is the number of vertices. I found Ted Spence's page on srgs, ...
1
vote
2answers
157 views

Regular graphs with strongly regular edge colorings

Given a positive integer $c>1$, for what parameters $(v,k,\lambda,\mu)$ does there exist a $c k$ regular graph on $v$ vertices that can be given an edge coloring with $c$ colors, such that the ...
1
vote
0answers
150 views

Articles on (Strongly Regular) Graphs and Covering Arrays / Covering Designs?

In their book "Algebraic Graph Theory" Godsil and Royle mention the connection of strongly regular graphs with latin squares and thus Orthogonal Arrays (Chapter 10.4). There seems not to be much ...
5
votes
2answers
510 views

What is the state of the art on triangle-free strongly regular graphs?

From what I've read I've gathered the following facts: There are seven known such graphs. Certain parameter sets are ruled out by the Krein conditions and the absolute bound. Beyond that, little or ...