4
votes
2answers
165 views

Estimate size of graph by taking random walks

Let $G$ be a connected, finite graph and let $v_0$ be a vertex of $G$. I'm interested in methods of estimating the number of vertices in $G$, based on local exploration only. What I have in mind is: ...
0
votes
0answers
258 views

Enumerating m-tuples of Integers Subject to Implication Constraints

How do I enumerate all $m$-tuples of positive integers $(a_1,...,a_m)$ subject to the following constraints? For each $i$ in \${ 1,\ldots,m }\$, there is a number $n_i \geq 0$ such that $a_i \leq ...
2
votes
4answers
7k views

Non-isomorphic graphs of given order.

It is well discussed in many graph theory texts that it is somewhat hard to distinguish non-isomorphic graphs with large order. But as to the construction of all the non-isomorphic graphs of any given ...