|
Search: id:A107459
|
|
|
| A107459 |
|
Number of nonisomorphic bipartite generalized Petersen graphs P(2n,k) with girth 6 on 4n vertices for 1<=k<n. |
|
+0
3
|
|
| 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2
(list; graph; listen)
|
|
|
OFFSET
|
4,5
|
|
|
COMMENT
|
The generalized Petersen graph P(n,k) is a graph with vertex set $V(P(n,k)) = \{u_0,u_1,\dots,u_{n-1},v_0,v_1,\dots,v_{n-1}\}$ and edge set $E(P(n,k)) = \{u_i u_{i+1}, u_i v_i, v_i v_{i+k} : i=0,\dots,n-1\},$ 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.
M. Watkins, A theorem on Tait colorings with an application to the generalized Petersen graphs, J. Combin. Theory 6 (1969), 152-164.
|
|
LINKS
|
Marko Boben, Tomaz Pisanski, Arjana Zitnik, I-graphs and the corresponding configurations, Preprint series (University of Ljubljana, IMFM), Vol. 42 (2004), 939 (ISSN 1318-4865).
|
|
EXAMPLE
|
A generalized Petersen graph P(n,k) is bipartite if and only if n is even and k is odd; it has girth 6 if and only if it has girth more than 4 and (n=6k or k=3 or 2k=n-2 or 3k=n+1 or 3k=n-1)
The smallest bipartite generalized Petersen graph with girth 6 is P(8,3)
|
|
CROSSREFS
|
Cf. A077105, A107452-A107460.
Sequence in context: A055734 A095772 A003640 this_sequence A087976 A117277 A033831
Adjacent sequences: A107456 A107457 A107458 this_sequence A107460 A107461 A107462
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), Tomaz Pisanski (Tomaz.Pisanski(AT)fmf.uni-lj.si) and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), May 26 2005
|
|
|
Search completed in 0.002 seconds
|
