‎darafsheh and assari in [normal edge-transitive cayley graphs on non-abelian groups of order 4p‎, ‎where $p$ is a prime number‎, ‎sci‎. ‎china math‎., ‎56 (1) (2013) 213-219.] classified the connected normal edge transitive and‎ ‎$frac{1}{2}-$arc-transitive cayley graph of groups of order $4p$‎. ‎in this paper we continue this work by classifying the‎ ‎connected cayley graph of groups of order...

In a non-complete graph $Gamma$, a vertex triple $(u,v,w)$ with $v$ adjacent to both $u$ and $w$ is called a $2$-geodesic if $uneq w$ and $u,w$ are not adjacent. The graph $Gamma$ is said to be   $2$-geodesic transitive if its automorphism group is transitive on arcs, and also on 2-geodesics. We first produce a reduction theorem for the family of $2$-geodesic transitive graphs of prime power or...

Contents Introduction 615 General definitions and notation 618 § 1. Shadow geometries of incidence geometries 619 § 2. Shadow geometries of chamber systems and their geometrical reali-zations 626 § 3. Interpreting the shadow geometries as tessellations. .. . 6 3 1 § 4. Transitive tessellations for reflection groups 636 § 5. The Delaney symbols of the tessellations with a transitive reflection g...

Let $G$ be an $n$-vertex oriented graph. $t(G)$ (respectively $i(G)$) the probability that a random set of $3$ vertices spans transitive triangle independent set). We prove $t(G) + i(G) \geq \frac{1}{9}-o_n(1)$. Our proof uses method flag algebras we supplement with several steps make it more easily comprehensible. also stability result and exact result. Namely, describe extremal construction, ...

Let P be a parabolic subgroup of a semisimple complex Lie group G defined by a subset Σ of simple roots of G, and let Eφ be a homogeneous vector bundle over the flag manifold G/P corresponding to a linear representation φ of P . Using Bott’s theorem, we obtain sufficient conditions on φ in terms of the combinatorial structure of Σ for some cohomology groups of the sheaf of holomorphic sections ...

For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

darafsheh and assari in [normal edge-transitive cayley graphs onnon-abelian groups of order 4p, where p is a prime number, sci. china math. {bf 56} (1) (2013) 213$-$219.] classified the connected normal edge transitive and $frac{1}{2}-$arc-transitive cayley graph of groups of order$4p$. in this paper we continue this work by classifying theconnected cayley graph of groups of order $2pq$, $p > q...