The triangular graph with nodes on a side is denoted . Tutte (1970) showed that the Chromatic
Polynomials of planar triangular graphs possess a Root close to
,
where is the Golden Mean. More precisely, if is the number of Vertices of , then
See also Lattice Graph
References
Le Lionnais, F. Les nombres remarquables. Paris: Hermann, 1983.
Tutte, W. T. ``On Chromatic Polynomials and the Golden Ratio.'' J. Combin. Theory 9, 289-296, 1970.