Generating connected and biconnected graphs
Abstract
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.
Keywords
Cite
@article{arxiv.0710.5711,
title = {Generating connected and biconnected graphs},
author = {Angela Mestre},
journal= {arXiv preprint arXiv:0710.5711},
year = {2013}
}
Comments
v4, v5: minor corrections; v3: 30 pages, substantially revised version; two new sections with alternative recursion formula for loopless graphs and with algorithmic considerations added; v2: 25 pages, substantially revised notation and terminology; new section with recursion formula for simple graphs added; appendixes added