- #1

skippy1729

## Main Question or Discussion Point

Hello, I am an old engineer with a curiosity about some of the background independent QG models, CDT, graphity, &ct. I try to patch up the holes in my mathematical background as I go along. I am looking for some books or other references that might help with the following question about the graphity model:

Suppose I pick a specific Hamiltonian, large N number of vertices, and am able to determine a state (graph) of low or least energy. Suppose the maximum valence of any vertex is small (say in the range of 5 to 10). The adjacency matrix will be a large sparse matrix of 0's and 1's. At this point one would like to determine if the graph is a regular or irregular lattice of some low dimension (possibly with a small number of "defects") or is some high dimensional "rats nest".

My gut feeling is that any algorithm to accomplish this will have a high computational complexity. Anyone know of a book on graph theory which might shed some light on this type of problem? I live hundreds of miles from a "good" library so I would like something available online or on Amazon.

Thanks for any suggestions. Skippy

Suppose I pick a specific Hamiltonian, large N number of vertices, and am able to determine a state (graph) of low or least energy. Suppose the maximum valence of any vertex is small (say in the range of 5 to 10). The adjacency matrix will be a large sparse matrix of 0's and 1's. At this point one would like to determine if the graph is a regular or irregular lattice of some low dimension (possibly with a small number of "defects") or is some high dimensional "rats nest".

My gut feeling is that any algorithm to accomplish this will have a high computational complexity. Anyone know of a book on graph theory which might shed some light on this type of problem? I live hundreds of miles from a "good" library so I would like something available online or on Amazon.

Thanks for any suggestions. Skippy