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...
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 ...
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...
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...