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On sum of powers of the Laplacian and signless Laplacian eigenvalues of graphs
"... Let G be a graph of order n with signless Laplacian eigenvalues q1,...,qn and Laplacian eigenvalues µ1,...,µn. It is proved that for any real number α with 0 < α � 1 or 2 � α < 3, the inequality qα 1 + · · · + qα n � µ α 1 + · · · + µαn holds, and for any real number β with 1 < β < 2 ..."
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Cited by 5 (1 self)
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Let G be a graph of order n with signless Laplacian eigenvalues q1,...,qn and Laplacian eigenvalues µ1,...,µn. It is proved that for any real number α with 0 < α � 1 or 2 � α < 3, the inequality qα 1 + · · · + qα n � µ α 1 + · · · + µαn holds, and for any real number β with 1 < β <
On the sum of signless Laplacian eigenvalues of a graph
"... For a simple graph G, let e(G) denote the number of edges and Sk(G) denote the sum of the k largest eigenvalues of the signless Laplacian matrix of G. We conjecture that for any graph G with n vertices, Sk(G) ≤ e(G) + k+1 2 for k = 1,..., n. We prove the conjecture for k = 2 for any graph, and for ..."
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For a simple graph G, let e(G) denote the number of edges and Sk(G) denote the sum of the k largest eigenvalues of the signless Laplacian matrix of G. We conjecture that for any graph G with n vertices, Sk(G) ≤ e(G) + k+1 2 for k = 1,..., n. We prove the conjecture for k = 2 for any graph
Eigenvalue bounds for the signless Laplacian
 Publ. Inst. Math. (Beograd
"... Abstract. We extend our previous survey of properties of spectra of signless Laplacians of graphs. Some new bounds for eigenvalues are given, and the main result concerns the graphs whose largest eigenvalue is maximal among the graphs with fixed numbers of vertices and edges. The results are present ..."
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Abstract. We extend our previous survey of properties of spectra of signless Laplacians of graphs. Some new bounds for eigenvalues are given, and the main result concerns the graphs whose largest eigenvalue is maximal among the graphs with fixed numbers of vertices and edges. The results
ON THE MAIN SIGNLESS LAPLACIAN EIGENVALUES Of A Graph
, 2013
"... A signless Laplacian eigenvalue of a graph G is called a main signless Laplacian eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, some necessary and sufficient conditions for a graph with one main signless Laplacian eigenvalue or two main signless La ..."
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A signless Laplacian eigenvalue of a graph G is called a main signless Laplacian eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, some necessary and sufficient conditions for a graph with one main signless Laplacian eigenvalue or two main signless
Signless Laplacians of finite graphs
, 2006
"... Let G be a simple graph with n vertices. The characteristic polynomial det(xI − A) of a (0,1)adjacency matrix A of G is called the characteristic polynomial of G and denoted by PG(x). The eigenvalues of A (i.e. the zeros of det(xI − A)) and the spectrum of A (which consists of the n eigenvalues) ar ..."
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Cited by 52 (2 self)
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will be called the Qspectrum. The matrix L = D − A is known as the Laplacian of G and is very much studied in the literature. The matrix A + D is called the signless Laplacian in [3] and appears very rarely in published papers. Graphs with the same spectrum of an associated matrix M are called cospectral graphs
THE SMALLEST SIGNLESS LAPLACIAN EIGENVALUE OF GRAPHS UNDER PERTURBATION
, 2012
"... In this paper, we investigate how the smallest signless Laplacian eigenvalue of a graph behaves when the graph is perturbed by deleting a vertex, subdividing edges or moving edges. ..."
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In this paper, we investigate how the smallest signless Laplacian eigenvalue of a graph behaves when the graph is perturbed by deleting a vertex, subdividing edges or moving edges.
THE SIGNLESS LAPLACIAN SEPARATOR OF GRAPHS
, 2011
"... The signless Laplacian separator of a graph is defined as the difference between the largest eigenvalue and the second largest eigenvalue of the associated signless Laplacian matrix. In this paper, we determine the maximum signless Laplacian separators of unicyclic, bicyclic and tricyclic graphs wi ..."
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The signless Laplacian separator of a graph is defined as the difference between the largest eigenvalue and the second largest eigenvalue of the associated signless Laplacian matrix. In this paper, we determine the maximum signless Laplacian separators of unicyclic, bicyclic and tricyclic graphs
Sciences mathématiques, No 30 SIGNLESS LAPLACIANS AND LINE GRAPHS
, 2005
"... Bulletin T.CXXXI de l’Académie serbe des sciences et des arts − 2005 ..."
Results 1  10
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220