Results 1  10
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17
MaximumWeightBasis Preconditioners
 Applications
, 2002
"... This paper analyzes a novel method for constructing preconditioners for diagonallydominant symmetric positivedefinite matrices. The method discussed here is based on a simple idea: we construct M by simply dropping offdiagonal nonzeros from A and modifying the diagonal elements to maintain a certa ..."
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Cited by 22 (7 self)
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This paper analyzes a novel method for constructing preconditioners for diagonallydominant symmetric positivedefinite matrices. The method discussed here is based on a simple idea: we construct M by simply dropping offdiagonal nonzeros from A and modifying the diagonal elements to maintain a certain rowsum property. The preconditioners are extensions of Vaidya's augmented maximumspanningtree preconditioners. The preconditioners presented here were als mentioned by Vaidya in an unpublished manuscript, but without a complete analysis. The preconditioners that we present have only O(n+ t&sup2;) nonzeros, where n is the dimension of the matrix and t is a parameter that ne can choose. Their construction is efficient and guarantees that the condition number of the preconditioned system is O(n&sup2;/t&sup2;) if the number of nonzeros per row in the matrix is bounded by a constant. We have developed an efficient algorithm to construct these preconditioners and we have implemented it. We used our implementation to solve a simple model problem; we show the combinatorial structure of the preconditioners and we present encouraging convergence results.
Coalition formation games with separable preferences
 Mathematical Social Sciences
, 2003
"... We provide sufficient conditions for the existence of stable coalitional structures in a purely hedonic game, that is in a coalition formation game such that players ’ preferences over coalitions are completely determined by the members of the coalition to which they belong. First, we show that the ..."
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Cited by 20 (0 self)
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We provide sufficient conditions for the existence of stable coalitional structures in a purely hedonic game, that is in a coalition formation game such that players ’ preferences over coalitions are completely determined by the members of the coalition to which they belong. First, we show that the existence of core stable and Nash stable solutions for the game depends on certain vector decompositions of the utility functions representing additively separable and symmetric preferences. Then, we generalize the results obtained and show that equilibria with the same qualitative features exist under much weaker restrictions on agents’ preferences. Finally, we examine the relationships between the properties we introduce and other conditions, already known in the literature, that guarantee the existence of stable partitions.
Kulkarni: Generalized matrix tree theorem for mixed graphs
 Linear Multilinear Algebra
, 1999
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Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a given order
, 2007
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Largest eigenvalue of a unicyclic mixed graph
 Appl. Math. J. Chinese Univ. (English Series
"... Using the result on Fiedler vectors of a simple graph, we obtain a property on the structure of the eigenvectors of a nonsingular unicyclic mixed graph corresponding to its least eigenvalue. With the property, we get some results on minimizing and maximizing the least eigenvalue over all nonsingular ..."
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Cited by 12 (8 self)
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Using the result on Fiedler vectors of a simple graph, we obtain a property on the structure of the eigenvectors of a nonsingular unicyclic mixed graph corresponding to its least eigenvalue. With the property, we get some results on minimizing and maximizing the least eigenvalue over all nonsingular unicyclic mixed graphs on n vertices with fixed girth. In particular, the graphs which minimize and maximize, respectively, the least eigenvalue are given over all such graphs with girth 3.
The signless Laplacian spectral radius for bicyclic graphs with k pendant vertices
, 2010
"... In this paper, we study the signless Laplacian spectral radius of bicyclic graphs with given number of pendant vertices and characterize the extremal graphs. ..."
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Cited by 9 (5 self)
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In this paper, we study the signless Laplacian spectral radius of bicyclic graphs with given number of pendant vertices and characterize the extremal graphs.
The Laplacian spectrum of a mixed graph
 LINEAR ALGEBRA AND ITS APPLICATIONS 353 (2002) 11–20
, 2002
"... In this paper, we discuss some properties of relations between a mixed graph and its line graph, which are used to characterize the Laplacian spectrum of a mixed graph. Then we present two sharp upper bounds for the Laplacian spectral radius of a mixed graph in terms of the degrees and the average 2 ..."
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Cited by 8 (0 self)
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In this paper, we discuss some properties of relations between a mixed graph and its line graph, which are used to characterize the Laplacian spectrum of a mixed graph. Then we present two sharp upper bounds for the Laplacian spectral radius of a mixed graph in terms of the degrees and the average 2degrees of vertices and we also determine some extreme graphs which attain these upper bounds.
On spectral integral variations of mixed graphs
 LINEAR ALGEBRA AND ITS APPLICATIONS 374 (2003) 307–316
, 2003
"... In this paper, we characterize the mixed graphs with exactly one Laplacian eigenvalue moving up by an integer and other Laplacian eigenvalues remaining invariant when an edge ..."
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Cited by 6 (6 self)
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In this paper, we characterize the mixed graphs with exactly one Laplacian eigenvalue moving up by an integer and other Laplacian eigenvalues remaining invariant when an edge
Combinatorial characterization of the null spaces of symmetric Hmatrices
 LINEAR ALGEBRA AND ITS APPLICATIONS
, 2004
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CONES OF CLOSED ALTERNATING WALKS AND TRAILS
"... Dedicated to the memory of Malka Peled Abstract. Consider a graph whose edges have been colored red and blue. Assign a nonnegative real weight to every edge so that at every vertex, the sum of the weights of the incident red edges equals the sum of the weights of the incident blue edges. The set of ..."
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Cited by 1 (1 self)
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Dedicated to the memory of Malka Peled Abstract. Consider a graph whose edges have been colored red and blue. Assign a nonnegative real weight to every edge so that at every vertex, the sum of the weights of the incident red edges equals the sum of the weights of the incident blue edges. The set of all such assignments forms a convex polyhedral cone in the edge space, called the alternating cone. The integral (respectively, {0, 1}) vectors in the alternating cone are sums of characteristic vectors of closed alternating walks (respectively, trails). We study the basic properties of the alternating cone, determine its dimension and extreme rays, and relate its dimension to the majorization order on degree sequences. We consider whether the alternating cone has integral vectors in a given box, and use residual graph techniques to reduce this problem to the one of searching for an alternating trail connecting two given vertices. The latter problem, called alternating reachability, is solved in a companion paper along with related results.