Every finite, self-dual, regular (or chiral) 4-polytope of type {3, q, 3} has a trivalent 3-transitive (or 2-transitive) medial layer graph. Here, by dropping self-duality, we obtain a construction for semisymmetric trivalent graphs (which are edgebut not vertex-transitive). In particular, the Gray graph arises as the medial layer graph of a certain universal locally toroidal regular 4-polytope.

A list is given of all semisymmetric (edgebut not vertex-transitive) connected finite cubic graphs of order up to 768. This list was determined by the authors using Goldschmidt’s classification of finite primitive amalgams of index (3, 3), and a computer algorithm for finding all normal subgroups of up to a given index in a finitely-presented group. The list includes several previously undiscov...

We prove that conformally semi-symmetric spacetimes are actually semisymmetric. We also present a complete refined classification of the semi-symmetric spacetimes. PACS numbers: 04.20.Cv, 02.40.Ky, 04.20.Jb

The object of the present paper is to study quasi-conformally flat generalized Sasakian-space-forms. Also we study quasi-conformally semisymmetric generalized Sasakian-space-forms. As a consequence of the results, we obtain some important corollaries.