# Graphs in Python, Sage and Magma (Seminar DM)

Graphs in Python, Sage and Magma

Tomaž Pisanski

Torek, 25. novembra 2014, od 10h do 12h, Plemljev seminar, Jadranska 19

Povzetek: We implemented several programs that may deal with general Haar graphs. The programs are written in Python but embedded in the system Sage. A Haar graph is a covering graph over a dipole. This means it can be described by a set S of voltages where each element s from S is assigned to one of the one of the arcs leading from a black vertex of a dipole to a white vertex of a dipole with k edges, such that | S | = k and each arc receives its voltage. Here S is a set taken from some group G. If X is a set on n vertices, then each faithful X-action of G gives rise to a derived graph H(S,G,X), called the Haar graph. In practice only two actions are considered:

1. G is a subgroup of the symmetric group Sym(X), generated by S. In this case S is simply a set of permutations of an n-set. We shorten notation to H(S) and call the derived graph a permutation Haar graph.
2. G is generated by S and acts on itself with the usual right regular action. We shorten the notation to H(S,G) and call the derived graph a G-Haar graph. In particular, the cyclic Haar graphs have been studied in the past by Hladnik, Marušič and Pisanski. Hladnik independently developed a theory that lead to the study of abelian Haar graphs.

Our system has possibility to work with special classes of Haar graphs, eg. permutation Haar graph, cyclic Haar graph and abelian Haar graphs.

We will also show how one can work with Python, Sage and Magma using data from the census of vertex-transitive graphs of Potočnik, Spiga and Verret.