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Pebbling graphs of fixed diameter
 J. Graph Theory
, 2014
"... Abstract Given a configuration of indistinguishable pebbles on the vertices of a connected graph G on n vertices, a pebbling move is defined as the removal of two pebbles from some vertex, and the placement of one pebble on an adjacent vertex. The mpebbling number of a graph G, πm(G), is the small ..."
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Cited by 2 (2 self)
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(G), is the smallest integer k such that for each vertex v and each configuration of k pebbles on G there is a sequence of pebbling moves that places at least m pebbles on v. When m = 1, it is simply called the pebbling number of a graph. We prove that if G is a graph of diameter d and k, m ≥ 1 are integers
Bipartite Regular Graphs with Fixed Diameter
"... For given nonnegative integers k and D, we consider the problem of determining n,(k, D) , the smallest number n for which there exists a kregular bipartite graph on n vertices with diameter D. We solve the problem for all pairs ( k, D) with D + 2 (mod 4) and D + 3 (mod 4), for all pairs ( k, D ..."
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For given nonnegative integers k and D, we consider the problem of determining n,(k, D) , the smallest number n for which there exists a kregular bipartite graph on n vertices with diameter D. We solve the problem for all pairs ( k, D) with D + 2 (mod 4) and D + 3 (mod 4), for all pairs ( k
A LOWER BOUND FOR THE SPECTRAL RADIUS OF GRAPHS WITH FIXED DIAMETER
, 2008
"... A lower bound for the spectral radius of graphs with fixed diameter ..."
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A lower bound for the spectral radius of graphs with fixed diameter
On the Randić Index of Unicyclic Graphs with Fixed Diameter
"... Abstract The Randić index R(G) of a graph G is the sum of the weights of all edges uv of G, where d(u) denotes the degree of the vertex u. In this paper, we give sharp lower bounds of Randić index of unicyclic graphs with n vertices and diameter d, which partly confirms a conjecture in [1] (MATCH ..."
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Abstract The Randić index R(G) of a graph G is the sum of the weights of all edges uv of G, where d(u) denotes the degree of the vertex u. In this paper, we give sharp lower bounds of Randić index of unicyclic graphs with n vertices and diameter d, which partly confirms a conjecture in [1] (MATCH
The 0/1Borsuk Conjecture is Generically True for Each Fixed Diameter
, 2000
"... In 1933 Karol Borsuk asked whether every compact subset of R d can be decomposed into d + 1 subsets of strictly smaller diameter. The 0/1Borsuk conjecture asks a similar question using subsets of the vertices of a d dimensional cube. Although counterexamples to both conjectures are known, we ..."
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In 1933 Karol Borsuk asked whether every compact subset of R d can be decomposed into d + 1 subsets of strictly smaller diameter. The 0/1Borsuk conjecture asks a similar question using subsets of the vertices of a d dimensional cube. Although counterexamples to both conjectures are known, we
OUTER BILLIARD AROUND A CURVILINEAR TRIANGLE WITH A FIXED DIAMETER
"... Abstract: We consider an outer billiard around a Reulaux triangle. We prove the existence of infinitely many periodic points accumulating at infinity. To do so we construct a return map from a strip into itself and we study its properties. We also show some numerical simulations which, in particula ..."
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Abstract: We consider an outer billiard around a Reulaux triangle. We prove the existence of infinitely many periodic points accumulating at infinity. To do so we construct a return map from a strip into itself and we study its properties. We also show some numerical simulations which, in particular, display heteroclinic intersections and Smale’s horseshoes.
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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with loops (undirected cycles). The algorithm is an exact inference algorithm for singly connected networks the beliefs converge to the cor rect marginals in a number of iterations equal to the diameter of the graph.1 However, as Pearl noted, the same algorithm will not give the correct beliefs for mul
1 Fixed diameter scan protocol preferable for retinal nerve fiber layer measurement by Optical Coherence Tomography in all sizes of optic discs
"... 2 Background:Retinal nerve fiber layer(RNFL) measurements using a fixeddiameter versus a userdefined scanprotocol of optical coherence tomography(Stratus OCT©) were compared in 32 normal, 62 glaucoma suspects and 36 glaucomatous eyes. Methods:Peripapillary RNFL thickness was measured using the st ..."
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2 Background:Retinal nerve fiber layer(RNFL) measurements using a fixeddiameter versus a userdefined scanprotocol of optical coherence tomography(Stratus OCT©) were compared in 32 normal, 62 glaucoma suspects and 36 glaucomatous eyes. Methods:Peripapillary RNFL thickness was measured using
The Average Distance in a Random Graph with Given Expected Degrees
"... Random graph theory is used to examine the “smallworld phenomenon”– any two strangers are connected through a short chain of mutual acquaintances. We will show that for certain families of random graphs with given expected degrees, the average distance is almost surely of order log n / log ˜ d whe ..."
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Cited by 289 (13 self)
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where ˜ d is the weighted average of the sum of squares of the expected degrees. Of particular interest are power law random graphs in which the number of vertices of degree k is proportional to 1/k β for some fixed exponent β. For the case of β> 3, we prove that the average distance of the power law
Results 1  10
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