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» The Number of Labeled 2-Connected Planar Graphs
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COMBINATORICS
2002
71views more  COMBINATORICS 2002»
13 years 4 months ago
The Number of Labeled 2-Connected Planar Graphs
Edward A. Bender, Zhicheng Gao, Nicholas C. Wormal...
GC
2010
Springer
13 years 3 months ago
Enumerative Properties of Rooted Circuit Maps
In 1966 Barnette introduced a set of graphs, called circuit graphs, which are obtained from 3-connected planar graphs by deleting a vertex. Circuit graphs and 3-connected planar g...
Zhicheng Gao, Han Ren
ISAAC
2005
Springer
123views Algorithms» more  ISAAC 2005»
13 years 10 months ago
Sampling Unlabeled Biconnected Planar Graphs
We present an expected polynomial time algorithm to generate a 2-connected unlabeled planar graph uniformly at random. To do this we first derive recurrence formulas to count the ...
Manuel Bodirsky, Clemens Gröpl, Mihyun Kang
CORR
2007
Springer
130views Education» more  CORR 2007»
13 years 4 months ago
On Computing the Distinguishing Numbers of Planar Graphs and Beyond: a Counting Approach
A vertex k-labeling of graph G is distinguishing if the only automorphism that preserves the labels of G is the identity map. The distinguishing number of G, D(G), is the smallest...
Vikraman Arvind, Christine T. Cheng, Nikhil R. Dev...
DM
2002
97views more  DM 2002»
13 years 4 months ago
Resonance graphs of catacondensed even ring systems are median
Let G be a planar embedded 2-connected graph. Then the vertices of its resonance graph R(G) are the 1-factors of G, two 1-factors being adjacent whenever their symmetric differenc...
Sandi Klavzar, Petra Zigert, Gunnar Brinkmann