2-CONNECTION & EULER

The formula V - E + F = 1 works for 2-connection as well as 3-connection and higher valent graphs. You can put as many 2-connected points into the edges of a graph as you want to and it still works. The averaged valence in a graph is always given by ‘p’ where pV = 2E and works for all possible 2-connected points in a graph. The averaged polygon size is given by ‘n’ where nF = 2E and this does not give the true averaged polygon size. But pV = 2E and nF = 2E does give the Schlaefli equation for graphs that I discovered and that can be obtained by substituting ‘p’ and ‘n’ into V - E + F = 1. A true averaged polygon size can be obtained by averaging over a counting of polygons in a given graph. Such an n(polygon) factor does not work in the Schlafli relation for graphs where nF = 2E is the definition that works by algebraic substitution. This is covered in my 2 graph theory papers I note here...

GRAPHS & POLYGONS

Trivalent and higher valent graphs follow the relations V - E + F = 1 and nF = 2E and pV = 2E, but polygons and other 2-connected graphs do not follow nF = 2E. Triangulated polygons all follow nF = 2E and pV = 2E etc. All the hydrides of C when polygonalized with a connection halo all follow these 3 relations except for divalent C molecules. There needs to be a way for accommodating 2-connection in such a scheme so that nF = 2E for all the graphs and hydrides of C. 

ETERNITY CIPHERS

The Eddington ratios encode mathematical ciphers that show physical reality is ultimately connected to a Platonic universe. No one knows yet what the 5 ciphers mean or why v/c is what it is, or why m/M is what it is. But everyone now knows these mathematical ciphers point to a Platonic ultimate reality for the universe and an equation of state for the universe that is a fifth order polynomial with 5 mathematically distinct roots. And so it goes.