In this paper, bounds for the edge connectivity of m-Cayley graphs are found, and also several structural conditions are given for a connected k-regular bi-abelian graph to have edge connectivity strictly less than k. Finally, two infinite families of partial sum families that generate directed strongly regular graphs with new parameters are shown.

COBISS.SI-ID: 1024291668

In this paper a subfamily of dihedrants, that is, Cayley graphs on dihedral groups, which admit a 1-regular subgroup of automorphisms is considered. The obtained results give important steps towards a possible complete classification of Cayley maps on dihedral groups.

COBISS.SI-ID: 1024277076

A bicirculant is a graph admitting an automorphism with exactly two vertex-orbits of equal size and no other orbit. All non-isomorphic 4-valent edge-transitive bicirculants are characterized in this paper. As a corollary, a characterization of 4-valent arc-transitive dihedrants is obtained.

COBISS.SI-ID: 1024316244