cp's OEIS Frontend

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.

A338604 Number of unlabeled connected graphs with n edges with degree >= 3 at each node.

This page as a plain text file.
%I A338604 #10 Nov 23 2020 17:08:22
%S A338604 1,0,1,3,5,9,27,67,198,646,2216,8178,32095,132093,568368,2541506,
%T A338604 11762657,56183633,276288402,1396172601,7238931364
%N A338604 Number of unlabeled connected graphs with n edges with degree >= 3 at each node.
%e A338604 a(10)=5:
%e A338604 There are 5 graphs with 10 edges and degree >=3 at all nodes (see table in A123545):
%e A338604 The complete graph on 5 nodes, given by the edge list
%e A338604 [[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],
%e A338604 and 4 graphs on 6 nodes:
%e A338604   [[1,3],[1,5],[1,6],[2,4],[2,5],[2,6],[3,5],[3,6],[4,5],[4,6]],
%e A338604   [[1,4],[1,5],[1,6],[2,4],[2,5],[2,6],[3,4],[3,5],[3,6],[4,6]],
%e A338604   [[1,3],[1,4],[1,6],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6],[5,6]],
%e A338604   [[1,3],[1,4],[1,5],[1,6],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6]].
%e A338604 The first one has degree 3 or 4 at all nodes, but becomes disconnected by removing nodes 5 and 6 and their incident edges. It is therefore not 3-connected.
%e A338604     .--5--.
%e A338604    /  / \  \
%e A338604   1--3   4--2
%e A338604    \  \ /  /
%e A338604     .--6--.
%e A338604 .
%e A338604 The complete graph on 5 nodes and the last 3 graphs with 6 nodes are all 3-connected. Thus A338511(10)=4, and by inclusion of the graph shown above a(10)=5.
%Y A338604 Cf. A007112, A123545, A338511, A338593, A338594.
%K A338604 nonn,hard,more
%O A338604 6,4
%A A338604 _Hugo Pfoertner_, Nov 21 2020