Generating connected and biconnected graphs

Details Generating connected and biconnected graphs Generating connected and biconnected graphs

2007-10-30

arxiv.org/abs/0710.5711v5

Journal of Graph Algorithms and Applications, Vol. 13, no. 2, pp. 251-281, 2009.

Mathematics

Combinatorics

v4, v5: minor corrections; v3: 30 pages, substantially revised version; two new sections with alternative recursion formula fo

Scientific paper

We focus on the algorithm underlying the main result of [A. Mestre, R. Oeckl, Generating loop graphs via Hopf algebra in quantum field theory. J. Math. Phys., 47, 122302, 2006]. This is an algebraic formula to generate all connected graphs in a recursive and efficient manner. The key feature is that each graph carries a scalar factor given by the inverse of the order of its group of automorphisms. In the present paper, we revise that algorithm on the level of graphs. Moreover, we extend the result subsequently to further classes of connected graphs, namely, (edge) biconnected, simple and loopless graphs. Our method consists of basic graph transformations only.

Affiliated with

Also associated with

No associations

Rating

Generating connected and biconnected graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Generating connected and biconnected graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Generating connected and biconnected graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-365911