Arjana Žitnik

Straight-ahead walks in Eulerian graphs

A straight-ahead walk in an embedded Eulerian graph G always passes from an edge to the opposite edge in the rotation at the same vertex. A straight-ahead walk is called Eulerian if all the edges of the embedded graph G are traversed in this way starting from an arbitrary edge. An embedding that contains an Eulerian straight-ahead walk is called an Eulerian embedding. In this article, we characterize some properties of Eulerian embeddings of graphs and of embeddings of graphs such that the corresponding medial graph is Eulerian embedded. We prove that in the case of 4-valent planar graphs, the number of straight-ahead walks does not depend on the actual embedding in the plane. Finally, we show that the minimal genus over Eulerian embeddings of a graph can be quite close to the minimal genus over all embeddings.

Distance-regular graphs of q-Racah type and the universal Askey–Wilson algebra

Let

Half-arc-transitive graphs of arbitrary even valency greater than 2

\C

The clone cover

denote the field of complex numbers, and fix a nonzero

Vertex-transitive graphs and their arc-types

q \in \C

Combinatorial configurations, quasiline arrangements, and systems of curves on surfaces

such that

Selected Open and Solved Problems in Computational Synthetic Geometry

q^4 \ne 1

I-graphs and the corresponding configurations

. Define a

Topics in Topological Graph Theory: Representing graphs and maps

\C

Isomorphism Checking of I -graphs

-algebra