A107460 - OEIS

%I #9 Jan 01 2019 15:20:33

%S 1,0,1,3,2,1,3,2,3,3,3,5,5,3,4,7,6,4,6,7,6,9,6,6,9,6,10,11,8,7,11,11,

%T 9,13,9,11,14,9,10,15,12,12

%N Number of nonisomorphic bipartite generalized Petersen graphs P(2n,k) with girth 8 on 4n vertices for 1<=k<n.

%C 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 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 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 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 A generalized Petersen graph P(n,k) is bipartite if and only if n is even and k is odd; it has girth 8 if and only if it has girth more than 6

%e The smallest bipartite generalized Petersen graph with girth 8 is P(18,5)

%Y Cf. A077105, A107452-A107459.

%K nonn

%O 9,4

%A Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), _Tomaz Pisanski_ and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), May 26 2005