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...

Constructing symmetric drawings of graphs is NP-hard. In this paper, we present a new method for drawing graphs symmetrically based on group theory. More formally, we define an n-geometric automorphism group as a subgroup of the automorphism group of a graph that can be displayed as symmetries of a drawing of the graph in n dimensions. Then we present an algorithm to find all 2and 3-geometric a...

This paper deals with the relation between the automorphism groups of some paving matroids and Z3, where Z3 is the additive group of modulo 3 over Z. It concludes that for paving matroids under most cases, Z3 is not isomorphic to the automorphism groups of these paving matroids. Even in the exceptional cases, we reasonably conjecture that Z3 is not isomorphic to the automorphism groups of the c...

Computational techniques are described for the automorphism groups of edge-weighted graphs. Fortran codes based on the manipulation of weighted adjacency matrices are used to compute the automorphism groups of several edge-weighted graphs. The code developed here took 37l/2 min of CPU time to generate 1 036 800 permutations in the automorphism group of an edge-weighted graph.

The polycirculant conjecture asserts that every vertex-transitive digraph has a semiregular automorphism, that is, a nontrivial automorphism whose cycles all have the same length. In this paper we investigate the existence of semiregular automorphisms of edge-transitive graphs. In particular, we show that any regular edge-transitive graph of valency three or four has a semiregular automorphism.

We determine the quantum automorphism groups of finite graphs. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual automorphism group. We get a quantum dihedral group D4.

We consider graded twisted Calabi-Yau algebras of dimension 3 which are derivation-quotient the form A=kQ/I, where Q is a quiver and I an ideal relations coming from taking partial derivatives superpotential on Q. define type (M,P,d) such algebra A, M incidence matrix quiver, P permutation giving action Nakayama automorphism A vertices d degree superpotential. study question what possible types...