Abstract The natural symmetries of Riemannian manifolds are described by the its Riemann curvature tensor. In that sense, most symmetric constant sectional ones. Its generalizations locally manifolds, semisymmetric and pseudosymmetric manifolds. analogous holomorphic Kaehler holomorphically Do they differ in some way from their analogues? Yes, we prove can all be characterized only terms planes...

The object of this paper is to study invariant submanifoldsM of Sasakian manifolds ̃ M admitting a semisymmetric nonmetric connection, and it is shown that M admits semisymmetric nonmetric connection. Further it is proved that the second fundamental forms σ and σ with respect to Levi-Civita connection and semi-symmetric nonmetric connection coincide. It is shown that if the second fundamental fo...

Suppose that Γ is a connected graph and G is a subgroup of the automorphism group Aut(Γ) of Γ. Then Γ is G-symmetric if G acts transitively on the arcs (and so the vertices) of Γ and Γ is G-semisymmetric if G acts edge transitively but not vertex transitively on Γ. If Γ is Aut(Γ)symmetric, respectively, Aut(Γ)-semisymmetric, then we say that Γ is symmetric, respectively, semisymmetric. If Γ is ...

An regular graph is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. In this paper we prove that for every prime p(6= 5), there is no semisymmetric cubic graph of order 4pn, where n ≥ 1. 2000 Mathematics Subject Classification: 05C25, 20B25.

For a group T and a subset S of T , the bi-Cayley graph BCay(T, S) of T with respect to S is the bipartite graph with vertex set T×{0, 1} and edge set {{(g, 0), (sg, 1)} | g ∈ T, s ∈ S}. In this paper, we investigate cubic bi-Cayley graphs of finite nonabelian simple groups. We give several sufficient or necessary conditions for a bi-Cayley graph to be semisymmetric, and construct several infin...

In this paper, we construct semisymmetric graphs in which no two vertices have exactly the same neighbors. We show how to do this by /rst considering bi-transitive graphs, and then we show how to choose two such graphs so that their product is regular. We display a family of bi-transitive graphs DN (a; b) which can be used for this purpose and we show that their products are semisymmetric by ap...