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488
An Algorithm for Cyclic Edge Connectivity of Cubic Graphs
, 2003
"... The cyclic edge connectivity is the size of the smallest edge cut in a graph such that at least two of the parts of the graph are not acyclic. We present an algorithm running in time O(n n) for computing the cyclic edge connectivity of nvertex cubic graphs. ..."
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The cyclic edge connectivity is the size of the smallest edge cut in a graph such that at least two of the parts of the graph are not acyclic. We present an algorithm running in time O(n n) for computing the cyclic edge connectivity of nvertex cubic graphs.
Wu: A polynomial algorithm for cyclic edge connectivity of cubic graphs
 Australasian Journal of Combinatorics
"... In this paper, we develop a polynomial time algorithm to find out all the minilnum cyclic edge cutsets of a 3regular graph, and therefore to determine the cyclic edge connectivity of a cubic graph. The algorithm is recursive, with complexity bounded by O(n31og2 n). The algorithm shows that the numb ..."
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In this paper, we develop a polynomial time algorithm to find out all the minilnum cyclic edge cutsets of a 3regular graph, and therefore to determine the cyclic edge connectivity of a cubic graph. The algorithm is recursive, with complexity bounded by O(n31og2 n). The algorithm shows
ON CYCLIC EDGECONNECTIVITY OF FULLERENES
, 2007
"... A graph is said to be cyclic kedgeconnected, if at least k edges must be removed to disconnect it into two components, each containing a cycle. Such a set of k edges is called a cyclickedge cutset and it is called a trivial cyclickedge cutset if at least one of the resulting two components ind ..."
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Cited by 8 (0 self)
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induces a single kcycle. It is known that fullerenes, that is, 3connected cubic planar graphs all of whose faces are pentagons and hexagons, are cyclic 5edgeconnected. In this article it is shown that a fullerene F containing a nontrivial cyclic5edge cutset admits two antipodal pentacaps, that is
Generating Unlabeled Connected Cubic Planar Graphs Uniformly at Random
"... We present an expected polynomial time algorithm to generate an unlabeled connected cubic planar graph uniformly at random. We first consider rooted connected cubic planar graphs, i.e., we count connected cubic planar graphs up to isomorphisms that fix a certain directed edge. Based on decompositi ..."
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We present an expected polynomial time algorithm to generate an unlabeled connected cubic planar graph uniformly at random. We first consider rooted connected cubic planar graphs, i.e., we count connected cubic planar graphs up to isomorphisms that fix a certain directed edge. Based
Improved bounds for the shortness coefficient of cyclically 4edge connected cubic graphs and snarks
, 2014
"... ..."
ON REMOVABLE EDGES IN 3−CONNECTED CUBIC GRAPHS
, 2012
"... A removable edge in a 3−connected cubic graph G is an edge e = uv such that the cubic graph obtained from G \ {u, v} by adding an edge between the two neighbours of u distinct from v and an edge between the two neighbours of v disctinct from u is still 3−connected. Li and Wu [3] showed that a span ..."
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Cited by 1 (0 self)
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A removable edge in a 3−connected cubic graph G is an edge e = uv such that the cubic graph obtained from G \ {u, v} by adding an edge between the two neighbours of u distinct from v and an edge between the two neighbours of v disctinct from u is still 3−connected. Li and Wu [3] showed that a
CYCLIC 7EDGECUTS IN FULLERENE GRAPHS
, 2009
"... A fullerene graph is a planar cubic graph whose all faces are pentagonal and hexagonal. The structure of cyclic edgecuts of fullerene graphs of sizes at most 6 is known. In the paper we study cyclic 7edge connectivity of fullerene graphs, distinguishing between degenerated and nondegenerated cycl ..."
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A fullerene graph is a planar cubic graph whose all faces are pentagonal and hexagonal. The structure of cyclic edgecuts of fullerene graphs of sizes at most 6 is known. In the paper we study cyclic 7edge connectivity of fullerene graphs, distinguishing between degenerated and non
Cubic graphs with large circumference deficit
, 2013
"... The circumference c(G) of a graph G is the length of a longest cycle. By exploiting our recent results on resistance of snarks, we construct infinite classes of cyclically 4, 5 and 6edgeconnected cubic graphs with circumference ratio c(G)/V (G) bounded from above by 0.876, 0.960 and 0.990, r ..."
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The circumference c(G) of a graph G is the length of a longest cycle. By exploiting our recent results on resistance of snarks, we construct infinite classes of cyclically 4, 5 and 6edgeconnected cubic graphs with circumference ratio c(G)/V (G) bounded from above by 0.876, 0.960 and 0
Connectivity of random cubic sum graphs
 SIAM J. Discrete Math
"... Consider the set SG(Qk) of all graphs whose vertices are labeled with nonidentity elements of the group Qk = Zk2 so that there is an edge between vertices with labels a and b if and only if the vertex labeled a + b is also in the graph. Note that edges always appear in triangles, since a + b = c, b ..."
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Cited by 1 (0 self)
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Consider the set SG(Qk) of all graphs whose vertices are labeled with nonidentity elements of the group Qk = Zk2 so that there is an edge between vertices with labels a and b if and only if the vertex labeled a + b is also in the graph. Note that edges always appear in triangles, since a + b = c
Fastest mixing markov chain on a graph
 SIAM REVIEW
, 2003
"... We consider a symmetric random walk on a connected graph, where each edge is labeled with the probability of transition between the two adjacent vertices. The associated Markov chain has a uniform equilibrium distribution; the rate of convergence to this distribution, i.e., the mixing rate of the ..."
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Cited by 155 (15 self)
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We consider a symmetric random walk on a connected graph, where each edge is labeled with the probability of transition between the two adjacent vertices. The associated Markov chain has a uniform equilibrium distribution; the rate of convergence to this distribution, i.e., the mixing rate
Results 1  10
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488