In this paper we develop the theory of polymorphisms of measure spaces, which is a generalization of the theory of measure-preserving transformations. We describe the main notions and discuss relations to the theory of Markov processes, operator theory, ergodic theory, etc. We formulate the important notion of quasi-similarity and consider quasi-similarity between polymorphisms and automorphism...

A finite simple graph Γ is called a Nest if it regular of valency 6 and admits an automorphism ρ with two orbits the same length such that at least one subgraphs induced by these cycle. We say core-free no non-trivial subgroup group generated normal in Aut(Γ). In this paper, we show that, edge-transitive core-free, then isomorphic to following graphs: complement Petersen graph, Hamming H(2,4), ...

We show that the full automorphism group of a circulant digraph of square-free order is either the intersection of two 2-closed groups, each of which is the wreath product of 2-closed groups of smaller degree, or contains a transitive normal subgroup which is the direct product of two 2-closed groups of smaller degree. The work in this paper makes contributions to the solutions of two problems ...

In this paper we introduce the concept of α-commutator which its definition is based on generalized conjugate classes. With this notion, α-nilpotent groups, α-solvable groups, nilpotency and solvability of groups related to the automorphism are defined. N(G) and S(G) are the set of all nilpotency classes and the set of all solvability classes for the group G with respect to different automorphi...

let d be a symmetric 2-(121, 16, 2) design with the automorphism group of aut(d). in this paper the order of automorphism of prime order of aut(d) is studied, and some results are obtained about the number of fixed points of these automorphisms. also we will show that |aut(d)|=2p 3q 5r 7s 11t 13u, where p, q, r, s, t and u are non-negative integers such that r, s, t, u ? 1. in addition we prese...

Interval graphs are intersection graphs of closed intervals and circle graphs are intersection graphs of chords of a circle. We study automorphism groups of these graphs. We show that interval graphs have the same automorphism groups as trees, and circle graphs have the same as pseudoforests, which are graphs with at most one cycle in every connected component. Our technique determines automorp...

In this paper an algorithm is presented that can be used to calculate the automorphism group of a finite transformation semigroup. The general algorithm employs a special method to compute the automorphism group of a finite simple semigroup. As an application of the algorithm, all the automorphism groups of semigroup of order at most 7 and of the multiplicative semigroups of some group rings ar...