This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385693 #18 Jul 24 2025 03:42:50
%S A385693 0,0,0,0,1,6,76,1990,84040,5749698
%N A385693 Number of prime graphs, G, on n vertices which do not contain a degree-1 vertex in G nor in co-G.
%C A385693 Here, "prime" means with respect to modular decomposition (see link).
%H A385693 GraphClasses, <a href="https://www.graphclasses.org/smallgraphs.html">List of Small Graphs</a>.
%H A385693 Wikipedia, <a href="https://en.wikipedia.org/wiki/Modular_decomposition">Modular decomposition</a>.
%e A385693 The smallest such graph is the cycle on 5 vertices. The 6 graphs on 6 vertices are the C6, domino, X37 (as named on GraphClasses) and their three respective complements.
%o A385693 (Sage)
%o A385693 for n in range(3, 11):
%o A385693 count = 0
%o A385693 for g in graphs.nauty_geng(f"{n} -c -d2"):
%o A385693 degrees = g.degree()
%o A385693 if max(degrees) < n-2 and g.is_prime():
%o A385693 count += 1
%o A385693 print(f"n = {n}: {count} prime graphs")
%Y A385693 Cf. A079473.
%K A385693 nonn,more
%O A385693 1,6
%A A385693 _Jim Nastos_ and _Clara Elliott_, Jul 07 2025