The concept of graph symmetry is explained in terms of the vertex automorphism group, which is a subgroup of the complete vertex permutation group. The automorphism group can be deduced from the automorphism partition of graph vertices. An algorithm is described which constructs the automorphism group of a graph from the automorphism vertex partitioning. The algorithm is useful especially for g...

Automorphism groupS of Hadamard matrices are related to automorphism groups of de.Jigns, and the automorphism groups of the Paley-Hadamard matrices are determined .

In this thesis, we investigate several properties of k-tournaments, where k 2 3. These properties fall into three broad areas. The first contains properties related to the ranking of the participants in a k-tournament, including a representation theorem for posets. The second contains properties related to the representation of a finite group as the automorphism group of a k-tournament, with va...

In this paper we use orderly algorithms to enumerate (perfect) one-factorizations of complete graphs, the automorphism groups of which contain certain prescribed subgroups. We showed that, for the complete graph Ki2, excluding those one-factorizations containing exactly one automorphism of six disjoint cycles of length two, there are precisely 56391 nonisomorphic one-factorizations of Ki2 with ...

The present paper deals with permutations induced by tame automorphisms over finite fields. The first main result is a formula for determining the sign of the permutation induced by a given elementary automorphism over a finite field. The second main result is a formula for determining the sign of the permutation induced by a given affine automorphism over a finite field. We also give a combini...

In this paper we shall present a natural generalisation of the notion of automorphism of a graph or digraph G, namely a two-fold automorphism. This is a pair (α, β) of permutations of the vertex set V(G) which acts on ordered pairs of vertices of G in the natural way. The action of (α, β) on all such ordered pairs gives a graph which is two-fold isomorphic to G. When α = β the two-fold automorp...

We describe a compactification by KSBA stable pairs of the five-dimensional moduli space K3 surfaces with purely non-symplectic automorphism order four and $U(2)\oplus D_4^{\oplus 2}$ lattice polarization. These can be realized as minimal resolution double cover $\mathbb {P}^{1}\times \mathbb {P}^{1}$ branched along specific $(4,\,4)$ curve. show that, up to finite group action, this is isomorp...

Scmicomplctc nilpotcnt groups, that is, nilpotent groups with no outer automorphisms, have been of interest for many years. In this paper pscudocomplete nilpotent groups, that is, nilpotent groups in which the automorphism group and the inner automorphism group arc isomorphic (not equal), are constructed. When suitable conditions are placed on the pseudocomplete nilpotent group, the quotient of...