A regular graph is called semisymmetric if it is edge transitive but not vertex transitive It is proved that the Gray graph is the only cubic semisymmetric graph of order p where p is a prime

Symmetric and semisymmetric graphs are used in many scientific domains, especially parallel computation and interconnection networks. The industry and the research world make a huge usage of such graphs. Constructing symmetric and semisymmetric graphs is a large and hard problem. In this paper a tool called G-graphs and based on group theory is used. We show the efficiency of this tool for cons...

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 ...

The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discuss...

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...

We derive matter collineations for some static spherically symmetric spacetimes and compare the results with Killing, Ricci and Curvature symmetries. We conclude that matter and Ricci collineations are not, in general, the same.

Riemannian manifolds with a Levi-Civita connection and constant Ricci curvature, or Einstein manifolds, were studied in the works of many mathematicians. This question has been most homogeneous case. In this direction, famous ones are results by D.V. Alekseevsky, M. Wang, V. Ziller, G. Jensen, H.Laure, Y.G. Nikonorov, E.D. Rodionov other At same time, studying little for case an arbitrary metri...