/explore
|
You are here 
|
junglyhh.wordpress.com | ||
| | | | |
www.jeremykun.com
For fixed integers $ r > 0$, and odd $ g$, a Moore graph is an $ r$-regular graph of girth $ g$ which has the minimum number of vertices $ n$ among all such graphs with the same regularity and girth. (Recall, A the girth of a graph is the length of its shortest cycle, and it's regular if all its vertices have the same degree) Problem (Hoffman-Singleton): Find a useful constraint on the relationship between $ n$ and $ r$ for Moore graphs of girth $ 5$ and degree $ r$. |
|
| | | | | ||
| | | | |
yufeizhao.com
How high can the second eigenvalue multiplicity of a connected bounded degree graph get? |
|
| | | | | ||
| | | | |
dominiczypen.wordpress.com
Suppose you want to have a graph $latex G = (V,E)$ with chromatic number $latex \chi(G)$ equaling some value $latex k$, such that $latex G$ is minimal with this property. So you end up with a $latex k$-(vertex-)critical graph. It is easy to construct critical graphs by starting with some easy-to-verify example like $latex C_5$... |
|
| | | | | ||
| | | | |
cardinalguzman.wordpress.com
Encyclopedia Miscellaneous - 'quality' blogging since August 2011 |
|
| | | |||
