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Handbook of Graph Drawing and Visualization
book

Handbook of Graph Drawing and Visualization

by Roberto Tamassia
August 2013
Intermediate to advanced content levelIntermediate to advanced
862 pages
32h 20m
English
Chapman and Hall/CRC
Content preview from Handbook of Graph Drawing and Visualization
3.4. FINDING GEOMETRIC AUTOMORPHISMS 97
First, suppose that G has a fixed point free automorphism β. It is clear that one can
extend β to G
to give an automorphism that satisfies part (a) of Theorem 3.2, and so G
has an axial geometric automorphism group.
Now suppose that G
has an axial geometric automorphism γ.
We claim that γ cannot map a vertex w of H to a vertex v of G, or to one of the new
vertices w
v
i
. This is bec aus e every vertex of G i s adjacent to a clique of size n + 1, while
no vertex of H has this property. Further, γ cannot map a vertex of G to one of the new
vertices w
v
i
, because each w
v
i
is in a clique of size n + 1, and none of the ...
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Publisher Resources

ISBN: 9781420010268