A107456 - OEIS

%I #9 Jan 01 2019 15:19:12

%S 1,1,1,1,2,1,2,1,3,2,2,0,2,2,2,4,2,1,2,2,2,2,5,1,2,2,2,2,2,4,2,2,2,2,

%T 2,1,5,2,2,2,2,1,2,5,2,2,2,1,2,2,5,2,2,1,2,2,2,5,2,1,2,2,2,2,5,1,2,2,

%U 2,2,2,4,2,2,2,2,2,1,5,2,2,2,2,1,2,5,2,2

%N Number of nonisomorphic generalized Petersen graphs P(n,k) with girth 7 on n vertices for 1<=k<=Floor[(n-1)/2].

%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) has girth 7 if and only if it has girth more than 6 and (n=7k or 2n=7*k or 3n=7k or k=4 or 4k=n+1 or 4=n-k or 4k=n-1 or 4k=2n-1 or 3k=n+2 or 3=n-2k or 3k=n-2)

%e The smallest generalized Petersen graph with girth 7 is P(13,5)

%Y Cf. A077105, A107452-A107460.

%K nonn

%O 13,5

%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