cp's OEIS Frontend

A107457 Triangle read by rows: row n gives number of nonisomorphic generalized Petersen graphs P(n,k) with girth 8 on n vertices for 1<=k<=floor[(n-1)/2].

%I A107457 #16 Aug 17 2020 19:49:14
%S A107457 1,0,0,1,2,1,4,1,4,3,2,3,4,3,5,6,7,2,7,5,8,8,8,6,8,6,10,9,11,7,13,6,
%T A107457 12,12,13,9,15,11,13,14,16,10,17,11,17,14,17,15,21,12,19,18,18,13,23,
%U A107457 14,22,20,22,16,26,15,24,21,25,16,26,21,26,24
%N A107457 Triangle read by rows: row n gives number of nonisomorphic generalized Petersen graphs P(n,k) with girth 8 on n vertices for 1<=k<=floor[(n-1)/2].
%C A107457 The generalized Petersen graph P(n,k) is a graph with vertex set V(P(n,k)) = {u_0,u_1,...,u_{n-1},v_0,v_1,...,v_{n-1}} and edge set E(P(n,k)) = {u_i u_{i+1}, u_i v_i, v_i v_{i+k} : i=0,...,n-1}, where the subscripts are to be read modulo n.
%D A107457 I. Z. Bouwer, W. W. Chernoff, B. Monson and Z. Star, The Foster Census (Charles Babbage Research Centre, 1988), ISBN 0-919611-19-2.
%H A107457 Marko Boben, Tomaz Pisanski, Arjana Zitnik, <a href="http://preprinti.imfm.si/PDF/00939.pdf">I-graphs and the corresponding configurations</a>, Preprint series (University of Ljubljana, IMFM), Vol. 42 (2004), 939 (ISSN 1318-4865).
%H A107457 B. Horvat, T. Pisanski; A. Zitnik.  <a href="https://doi.org/10.1007/s00373-011-1086-2">Isomorphism checking of I-graphs</a>, Graphs Comb. 28, No. 6, 823-830 (2012).
%H A107457 M. Watkins, <a href="https://doi.org/10.1016/S0021-9800(69)80116-X">A theorem on Tait colorings with an application to the generalized Petersen graphs</a>, J. Combin. Theory 6 (1969), 152-164.
%e A107457 Any generalized Petersen graph P(n,k) has girth at most 8; it has girth 8 if and only if it has girth more than 7.
%e A107457 The smallest generalized Petersen graph with girth 8 is P(18,5)
%Y A107457 Cf. A077105, A107452-A107460.
%K A107457 nonn,tabf
%O A107457 18,5
%A A107457 Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), _Tomaz Pisanski_ and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), May 26 2005
%E A107457 Example corrected by Greg Demand, Jan 17 2008
%E A107457 Typo in description corrected by _Harvey P. Dale_, Aug 17 2020