Crosscovers

Aleksander Malnič (University of Ljubljana, Slovenia)

To each unoriented edge e of a connected graph $X$ assign an element $\zeta_e$ from a given abelian group $\Gamma$. The graph $X(\Gamma,\zeta)$ with $V(X) \times\Gamma$ as the vertex set, where $(u,g)$ and $(v,h)$ are adjacent whenever there is an edge $e = uv$ in $X$ and $g+h = \zeta_e$, is called a crosscover. Crosscovers, an obvious generalization of Cayley sum graphs, are a special kind of covers. Some basic facts like regularity/irregularity, connectedness, and lifting automorphisms will be discussed.

This is joint work with Steve Wilson.