We show that the automorphism group of a divisible design D is isomorhic to a subgroup H of index 1 or 2 in the automorphism group Aut C(D) of the associated constant weight code. Only in very special cases, H is not the full automorphism group.

The aim of this paper is to show that the automorphism and isometry groups of the suspension of B(H), H being a separable infinite dimensional Hilbert space, are algebraically reflexive. This means that every local automorphism, respectively local surjective isometry of C0(R) ⊗ B(H) is an automorphism, respectively a surjective isometry.

The expected n-step return-probability EμP [X̂n = o] of a random walk X̂n with symmetric transition probabilities on a random partial graph of a regular graph G of degree δ with transitive automorphism group Aut(G) is considered. The law μ of the random edge-set is assumed to be stationary with respect to some transitive, unimodular subgroup Γ of Aut(G). By the spectral theory of finite random wa...

Denote the n × n toroidal queen’s graph by Qn. We find its automorphism group Aut(Qn) for each positive integer n, showing that for n ≥ 6, Aut(Qn) is generated by the translations, the group of the square, the homotheties, and (for odd n) the automorphism (x, y) → (y + x, y − x). For each n we find the automorphism classes of edges of Qn, in particular showing that for n > 1, Qn is edge-transit...

in this paper we study the coprime graph of a group $g$. the coprime graph of a group $g$, is a graph whose vertices are elements of $g$ and two distinct vertices $x$ and $y$ are adjacent iff $(|x|,|y|)=1$. in this paper we classify all the groups which the coprime graph is a complete r-partite graph or a planar graph. also we study the automorphism group of the coprime graph.

abstract let ‎g=(v,e) ‎be a‎ ‎simple ‎connected ‎graph ‎with ‎vertex ‎set ‎v‎‎‎ ‎and ‎edge ‎set ‎‎‎e. ‎the szeged index ‎of ‎‎g is defined by ‎ where ‎ respectively ‎ ‎ is the number of vertices of ‎g ‎closer to ‎u‎ (‎‎respectively v)‎ ‎‎than ‎‎‎v (‎‎respectively u‎).‎ ‎‎if ‎‎‎‎s ‎is a‎ ‎set ‎of ‎size‎ ‎ ‎ ‎let ‎‎v ‎be ‎the ‎set ‎of ‎all ‎subsets ‎of ‎‎s ‎of ‎size ‎3. ‎then ‎we ‎define ‎three ‎...

The purpose of this paper is to complete the classification of binary self-dual [48, 24, 10] codes with an automorphism of odd prime order. We prove that if there is a self-dual [48, 24, 10] code with an automorphism of type p-(c, f) with p being an odd prime, then p = 3, c = 16, f = 0. By considering only an automorphism of type 3-(16, 0), we prove that there are exactly 264 inequivalent self-...

A graph Γ=(V,E) of order n is distance magic if it admits a bijective labeling ℓ:V→{1,2,…,n} its vertices for which there exists positive integer κ such that ∑u∈N(v)ℓ(u)=κ all v∈V, where N(v) the neighborhood v. circulant admitting an automorphism cyclically permuting vertices. In this paper we study circulants valency 6. We obtain some necessary and sufficient conditions 6 to be magic, thereby...