cp's OEIS Frontend

A184945 Number of connected 4-regular simple graphs on n vertices with girth exactly 5.

%I A184945 #15 Jan 25 2024 12:54:00
%S A184945 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,8,131,3917,123859,4131991,
%T A184945 132160607,4018022149,118369811959
%N A184945 Number of connected 4-regular simple graphs on n vertices with girth exactly 5.
%H A184945 Jan Goedgebeur and Jorik Jooken, <a href="https://arxiv.org/abs/2401.08271">Exhaustive generation of edge-girth-regular graphs</a>, arXiv:2401.08271 [math.CO], 2024. See p. 12.
%H A184945 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_eq_g_index">Index of sequences counting connected k-regular simple graphs with girth exactly g</a>
%F A184945 a(n) = A058343(n) - A058348(n).
%e A184945 a(0)=0 because even though the null graph (on zero vertices) is vacuously 4-regular and connected, since it is acyclic, it has infinite girth.
%e A184945 The a(19)=1 graph is the unique (4,5) cage: the Robertson graph (see also A159191). It has the following adjacency lists.
%e A184945 01 : 02 03 04 05
%e A184945 02 : 01 06 07 08
%e A184945 03 : 01 09 10 11
%e A184945 04 : 01 12 13 14
%e A184945 05 : 01 15 16 17
%e A184945 06 : 02 09 12 15
%e A184945 07 : 02 10 13 16
%e A184945 08 : 02 11 14 17
%e A184945 09 : 03 06 13 17
%e A184945 10 : 03 07 14 18
%e A184945 11 : 03 08 16 19
%e A184945 12 : 04 06 16 18
%e A184945 13 : 04 07 09 19
%e A184945 14 : 04 08 10 15
%e A184945 15 : 05 06 14 19
%e A184945 16 : 05 07 11 12
%e A184945 17 : 05 08 09 18
%e A184945 18 : 10 12 17 19
%e A184945 19 : 11 13 15 18
%Y A184945 4-regular simple graphs with girth exactly 5: this sequence (connected), A185045 (disconnected), A185145 (not necessarily connected).
%Y A184945 Connected k-regular simple graphs with girth exactly 5: A006925 (k=3), this sequence (k=4), A184955 (k=5).
%Y A184945 Connected 4-regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), A058343 (g=5), A058348 (g=6).
%Y A184945 Connected 4-regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), this sequence (g=5).
%K A184945 nonn,hard,more
%O A184945 0,21
%A A184945 _Jason Kimberley_, Feb 14 2011