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Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.
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What is the number of connected graphs with $n$ vertices of max. degree up to $D$? Leaving $...
It is known that $F(x)$ is the generating function of the counting sequence of connected simple graphs with N vertices is given by:
$F(x) = x + x^2 + 2x^3 + 6x^4 + 21x^5 + 112x^6 + 853x^7...$
where th …