2014/12/05 by Julien Courtiel, Courtiel, Julien
Mathematics · Physics and Astronomy · #Graph theory and applications #Mathematical Dynamics and Fractals #Theoretical and Computational Physics #math.CO
paper · pdf · doi:10.48550/arxiv.1412.2081
38 pages, 21 figures
arxiv created 2014/12/05 · arxiv updated 2014/12/08
In the literature can be found several descriptions of the Tutte polynomial of graphs. Tutte defined it thanks to a notion of activity based on an ordering of the edges. Thereafter, Bernardi gave a non-equivalent notion of the activity where the graph is embedded in a surface. In this paper, we see that other notions of activity can thus be imagined and they can all be embodied in a same notion, the Δ-activity. We develop a short theory which sheds light on the connections between the different expressions of the Tutte polynomial.