Abstract In this article we consider the Directed Steiner Path Cover problem on directed co-graphs. Given a graph $$G=(V,E)$$ G = ( V , E ) and set $$T \subseteq V$$ T ...

The canonical double cover $B(X)$ of a graph $X$ is the direct product and $K_2$. If $Aut(B(X)) \cong Aut(X) \times \mathbb{Z}_2$ then called stable; otherwise unstable. An unstable nontrivially if it connected, non-bipartite distinct vertices have different neighborhoods. Circulant Cayley on cyclic group. Qin et al. conjectured in [J. Combin. Theory Ser. B 136 (2019), 154-169] that there are n...

Abstract Motivated by the problem of finding algebraic constructions finite coverings in commutative algebra, Steinitz realization number theory and study Hurwitz spaces geometry, we investigate vector bundles underlying structure sheaf a flat branched covering. We prove that, up to twist, every bundle on smooth projective curve arises from direct image smooth, connected cover.