OFFSET
2,3
COMMENTS
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.
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 and Arjana Zitnik, I-graphs and the corresponding configurations, Preprint series (University of Ljubljana, IMFM), Vol. 42 (2004), 939 (ISSN 1318-4865).
B. Horvat, T. Pisanski; A. Zitnik. Isomorphism checking of I-graphs, Graphs Comb. 28, No. 6, 823-830 (2012).
M. Watkins, A theorem on Tait colorings with an application to the generalized Petersen graphs, J. Combin. Theory 6 (1969), 152-164.
EXAMPLE
A generalized Petersen graph P(n,k) is bipartite if and only if n is even and k is odd.
The smallest bipartite generalized Petersen graph is P(4,1)
CROSSREFS
KEYWORD
nonn
AUTHOR
Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), Tomaz Pisanski and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), May 26 2005
STATUS
approved