This graceful graph is a favorite example that accompanies texts
on graphs.
It is triangle-free (its shortest girth is of length 4), and it is 2-colorable.
Help! What is the origin of this graph? [note].
The harmonic evolution digraph consists of:
| Loops | = | 4 L1 + 6 L2 | |
| Tree | = | T13 * T22 |
Note
Herschel is the surname a family of British astronomers.
This includes Sir William Herschel (1738-1822),
who discovered Uranus (1781) and cataloged numerous double stars and nebulae.
His sister Caroline Herschel (1750-1848) published a star catalog,
and his son Sir John Frederick William Herschel (1792-1871)
discovered another half-thousand nebulae
and conducted research on astrophysics, light, and photography.
Is the author the Herschel graph related to any of the above?
("Graph Theory 1736-1936" by N.L.Biggs at al., does not mention "Herschel's graph,"
but its bibliography includes a 1862 paper on Hamilton's icosian game by a certain
A.S. Herschel. The date of publication does not seem to match
Sir William-astronomer's life span.
Please send me a note
if you can cast some light on this puzzle.
Remark:
Discovery of Uranus was a shock to the astrological systems.
The East still ignores it. The West absorbed it, gave it
a symbol
and associated with
unpredictability, modern science, anarchy
and the destruction of the established order.
This is partially credited to the French Revolution
that occurred a few years after the discovery.
The symbol -- another "Herschel's graph" -- is modeled after "H".