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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
92 CHAPTER 3. SYMMETRIC GRAPH DRAWING
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Figure 3.3 A cir cu lar grid.
(c) A can be displayed as a dihedral group if and only if all the following conditions
hold.
i. A is dihedral; that is, it has two generators α and ρ such that α
2
= 1, ρ
k
= 1
for some k > 1, and αρ = ρ
1
α.
ii. |f ix
A
| 1.
iii. f ix
α
induces a set of disjoint paths.
iv. If ρ fixes an edge, then |fix
A
| = 0.
The proof of Theorem 3.2 is an algorithm, stated below, that takes a grap h G and an
automorphism grou p A satisfying the conditions of the theorem, and draws G to di sp lay A.
The drawing is on a circular grid as illustr ate d in Figure 3.3.
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Publisher Resources

ISBN: 9781420010268