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On the skew Laplacian energy of a digraph
 International Math. Forum
, 2009
"... In this paper we introduce the concept of the skew Laplacian energy of a simple, connected digraph. We derive an explicit formula for the skew Laplacian energy of a digraph G. We also find the minimal value of this energy in the class of all connected digraphs on n ≥ 2 vertices. Mathematics Subject ..."
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Cited by 4 (2 self)
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In this paper we introduce the concept of the skew Laplacian energy of a simple, connected digraph. We derive an explicit formula for the skew Laplacian energy of a digraph G. We also find the minimal value of this energy in the class of all connected digraphs on n ≥ 2 vertices. Mathematics Subject
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
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Cited by 801 (1 self)
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The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such
ON SOME INEQUALITIES FOR THE SKEW LAPLACIAN ENERGY OF DIGRAPHS
"... ABSTRACT. In this paper we introduce and investigate the skew Laplacian energy of a digraph. We establish upper and lower bounds for the skew Laplacian energy of a digraph. Key words and phrases: Digraphs, skew energy, skew Laplacian energy. 2000 Mathematics Subject Classification. 05C50, 05C90. 1. ..."
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ABSTRACT. In this paper we introduce and investigate the skew Laplacian energy of a digraph. We establish upper and lower bounds for the skew Laplacian energy of a digraph. Key words and phrases: Digraphs, skew energy, skew Laplacian energy. 2000 Mathematics Subject Classification. 05C50, 05C90. 1.
On the spectra of the Laplacian matrices of a certain class
"... A Laplacian matrix L = (ℓij) ∈ R n×n has nonpositive offdiagonal entries and zero row sums. Let Lα = (lij) be a Laplacian matrix defined as ..."
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A Laplacian matrix L = (ℓij) ∈ R n×n has nonpositive offdiagonal entries and zero row sums. Let Lα = (lij) be a Laplacian matrix defined as
On Laplacian Energy of Certain Mesh Derived Networks
"... Eigenvalues of a graph are the eigenvalues of its adjacency matrix. The multiset of eigenvalues is called its spectrum. There are many properties which can be explained using the spectrum like energy, connectedness, vertex connectivity, chromatic number, perfect matching etc. Laplacian spectrum is t ..."
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Eigenvalues of a graph are the eigenvalues of its adjacency matrix. The multiset of eigenvalues is called its spectrum. There are many properties which can be explained using the spectrum like energy, connectedness, vertex connectivity, chromatic number, perfect matching etc. Laplacian spectrum
Forest matrices around the Laplacian matrix
 Linear Algebra and Its Applications
"... We study the matrices Q k of inforests of a weighted digraph Γ and their connections with the Laplacian matrix L of Γ. The (i, j) entry of Q k is the total weight of spanning converging forests (inforests) with k arcs such that i belongs to a tree rooted at j. The forest matrices, Q k, can be calc ..."
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Cited by 19 (9 self)
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We study the matrices Q k of inforests of a weighted digraph Γ and their connections with the Laplacian matrix L of Γ. The (i, j) entry of Q k is the total weight of spanning converging forests (inforests) with k arcs such that i belongs to a tree rooted at j. The forest matrices, Q k, can
DETERMINATE SYSTEMS Coordination in multiagent systems and Laplacian spectra of digraphs
, 2008
"... Abstract—Constructing and studying distributed control systems requires the analysis of the Laplacian spectra and the forest structure of directed graphs. In this paper, we present some basic results of this analysis partially obtained by the present authors. We also discuss the application of these ..."
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Abstract—Constructing and studying distributed control systems requires the analysis of the Laplacian spectra and the forest structure of directed graphs. In this paper, we present some basic results of this analysis partially obtained by the present authors. We also discuss the application
Results 1  10
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