… the notion of automorphism of a graph or digraph G, namely a two-fold automorphism. This
… The action of (α, β) on all such ordered pairs gives a graph which is two-fold isomorphic to G…

… We will refer to this group as two-fold projections and use symbol Autπ(Γ) to … two-fold
automorphisms, especially we introduce the idea of the topological automorphisms of a graph …

… The set of all TF-automorphisms of G with … called the two-fold automorphism group of G and
is denoted by AutTFG. Note that if we identify an automorphism α with the TFautomorphism (α…

… Two-fold isomorphisms and automorphisms Two (mixed) graphs G and H are said to be
two-fold isomorphic or TF-isomorphic if there exist bijections a and β from V(G) to V(H) such that (…

… the automorphism … two-fold orbital graphs because whereas in orbital graphs the components
are clearly all isomorphic, a very different behaviour is observed for two fold orbital graphs. …

… The OS(TTS(6)) is unique up to isomorphism and has automorphism group of order 5 [18];
an example is given in Table 3. The automorphism group of this particular OS(TTS(6)) is …

… A special thanks goes to Russell Mizzi for help with overhauling Chapter 6, where we also
introduce the new idea of two-fold isomorphisms, and to Leonard Soicher and Matan Zif-Av for …

… an automorphism of r3, we have g(x) =f 0 #x 0 f-’ =fxf- ‘. Hence g: A, + A is an isomorphism
obtained by restricting the inner automorphism … This is a two-fold covering and it is compatible …

… in Section 4 at the automorphism group of the canonical double covering graph and discuss
the … GÄG which erases the second coordinate is a two-fold covering projection. Moreover, a …

… ) of graphs each having twice as many vertices and edges as G , and each having a two-fold …
One can regard work on the automorphism group of G as the study of (l:l) morphisms onto G …