A153847 Number of non-isomorphic connected I-graphs I(n,j,k) on 2n vertices (1<=j,k<=Floor[(n-1)/2]).

1, 1, 2, 2, 2, 3, 3, 4, 3, 7, 4, 5, 7, 6, 5, 8, 5, 10, 9, 8, 6, 14, 8, 10, 9, 13, 8, 19, 8, 12, 13, 13, 13, 19, 10, 14, 15, 20, 11, 25, 11, 19, 19, 17, 12, 26, 14, 22, 19, 22, 14, 26, 19, 26, 21, 22, 15, 40, 16, 23, 25, 24, 23, 37, 17, 28, 25, 37, 18, 38, 19, 28, 31, 31, 25, 43, 20

Offset: 3

Author

Tomaz Pisanski, Jan 08 2009

Keywords

• nonn

Comments

The I-graph I(n,j,k) is a graph with vertex set V(I(n,j,k)) = {u_0,u_1,...,u_{n-1},v_0,v_1,...,v_{n-1}} and edge set E(I(n,j,k)) = {u_i u_{i+j}, u_i v_i, v_i v_{i+k} : i=0,...,n-1}, where the subscripts are to be read modulo n. The I-graphs generalize the family of generalized Petersen graphs.

References

• I. Z. Bouwer, W. W. Chernoff, B. Monson and Z. Star, The Foster Census (Charles Babbage Research Centre, 1988), ISBN 0-919611-19-2.

Links

• Marko Boben, Tomaz Pisanski, Arjana Zitnik, I-graphs and the corresponding configurations J. Combin. Des. 13 (2005), no. 6, 406--424.
• M. Watkins, A theorem on Tait colorings with an application to the generalized Petersen graphs, J. Combin. Theory 6 (1969), 152-164.
• Eric Weisstein's World of Mathematics, Graph Expansion

Crossrefs

Cf. A077105, A153846.