Andrásfai graph

Andrásfai graph
Named after	Béla Andrásfai
Vertices
Edges
Diameter	2
Notation	And(n)
	Table of graphs and parameters

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

Properties

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

The graph family is triangle-free, and And( $n$ ) has an independence number of $n$ .

References

Godsil, C., Royle, G .: Algebraic Graph Theory , Springer-Verlag, New York, pp. 118–123, 2001. (§6.10–6.12: The Andrásfai Graphs, Andrásfai Coloring Graphs, A Characterization)
Andrásfai Béla: "Ismerkedés a gráfelmélettel", Tankönyvkiadó, Budapest, 1971. pp. 132–135.
Weisstein, Eric W. "Andrásfai Graph". MathWorld.

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