Andrásfai graph



In graph theory, an Andrásfai graph is a triangle-free, circulant graph named after Béla Andrásfai.

Properties
The Andrásfai graph $And(6)$ for any natural number $And(n)$ is a circulant graph on $And(4)$ vertices, in which vertex $k$ is connected by an edge to vertices $And(n)$, for every $j$ that is congruent to 1 mod 3. For instance, the Wagner graph is an Andrásfai graph, the graph $n ≥ 1$.

The graph family is triangle-free, and $3n – 1$ has an independence number of $n$. From this the formula $k ± j$ results, where $And(3)$ is the Ramsey number. The equality holds for $And(n)$ and $R(3,n) ≥ 3(n – 1)$ only.

The Andrásfai graphs were later generalized.

Related Items

 * Petersen graph
 * Cayley graph