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1 vote
1 answer
1k views

How many non-isomorphic, simple, connected graphs with 6 vertices are there? [closed]

A graph is called simple if there are no loops and there are no multiple edges. Is it possible to compute the number of non-isomorphic, simple, connected graphs with 6 vertices? If the number is known,...
2 votes
3 answers
284 views

Making integer multisets graphic

Let $M=(X,f)$ be a multiset, where $X$ is the underlying set of elements and $f:X\rightarrow\mathbb{N}$ is the multiplicity function. For every $k\in\mathbb{N}$ put $k\cdot M:=(X,k\cdot f)$. It is ...
5 votes
1 answer
384 views

Flow of an integer

I've stumbled across this family of flow networks, and posted the sequence of maximal flows to OEIS: A238729. I can't find any reference to it either. Has anyone seen it? Here is the description: ...
7 votes
2 answers
964 views

Maximal number of edges and triangular cells for n points in a triangular lattice

Consider a subset of $n$ points in an equilateral triangular lattice. Draw all the edges between nearest-neighbor points. What is the maximum, over all such subsets, of the number of edges? This ...