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The Extremal Structures of r-Uniform Unicyclic Hypergraphs on the Signless Laplacian Estrada Index
Mathematics, 2022 SLEE has various applications in a large variety of problems. The signless Laplacian Estrada index of a hypergraph H is defined as SLEE(H)=∑i=1neλi(Q), where λ1(Q),λ2(Q),…,λn(Q) are the eigenvalues of the signless Laplacian matrix of H. In this paper, we
Hongyan Lu, Zhongxun Zhu
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On maximum signless Laplacian Estrada index of graphs with given parameters II [PDF]
Electronic Journal of Graph Theory and Applications, 2018 The signless Laplacian Estrada index of a graph G is defined as SLEE(G) = ∑ni = 1eqi where q1, q2, …, qn are the eigenvalues of the signless Laplacian matrix of G.
Ramin Nasiri +3 more
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On the Signless Laplacian ABC-Spectral Properties of a Graph
MathematicsIn the paper, we introduce the signless Laplacian ABC-matrix Q̃(G)=D¯(G)+Ã(G), where D¯(G) is the diagonal matrix of ABC-degrees and Ã(G) is the ABC-matrix of G. The eigenvalues of the matrix Q̃(G) are the signless Laplacian ABC-eigenvalues of G.
Bilal A. Rather +2 more
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On the second largest eigenvalue of the signless Laplacian
Linear Algebra and its Applications, 2013 Let $G$ be a graph of order $n,$ and let $q_{1}(G) \geq ...\geq q_{n}(G) $ be the eigenvalues of the $Q$-matrix of $G$, also known as the signless Laplacian of $G.$ In this paper we give a necessary and sufficient condition for the equality $q_{k}(G) =n-2,$ where ...
de Lima, Leonardo Silva +1 more
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On Generalized Harary Eigenvalues and Generalized Join of Graphs
Journal of MathematicsIn this work, we further study the generalized Harary matrix of a connected graph G, which we denote by RDαG. This matrix is defined as the convex combination RDαG=αRTG+1−αRDG, where 0≤α≤1.
Abdollah Alhevaz +3 more
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Color signless Laplacian energy of graphs
AKCE International Journal of Graphs and Combinatorics, 2017 In this paper, we introduce the new concept of color Signless Laplacian energy . It depends on the underlying graph and the colors of the vertices. Moreover, we compute color signless Laplacian spectrum and the color signless Laplacian energy of families
Pradeep G. Bhat, Sabitha D’Souza
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Spectral Properties of the Harary Signless Laplacian and Harary Incidence Energy
MathematicsLet X be a partitioned matrix and let B its equitable quotient matrix. Consider a simple, undirected, connected graph G of order n. In this paper, we employ a technique based on quotient matrices derived from block-partitioned structures to establish new
Luis Medina +2 more
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Distance signless Laplacian eigenvalues, diameter, and clique number [PDF]
Discrete Mathematics Letters, 2022 Summary: Let \(G\) be a connected graph of ordern. Let \(\operatorname{Diag}(\mathrm{Tr})\) be the diagonal matrix of vertex transmissions and let \(\mathcal{D}(G)\) be the distance matrix of \(G\). The distance signless Laplacian matrix of \(G\) is defined as \(\mathcal{D}^{\mathcal{Q}}(G) =\operatorname{Diag}(\mathrm{Tr}) + \mathcal{D}(G)\) and the ...
Saleem Khan, Shariefuddin Pirzada
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On the main signless Laplacian eigenvalues of a graph [PDF]
The Electronic Journal of Linear Algebra, 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, we first give the necessary and sufficient conditions for a graph with one main signless Laplacian eigenvalue or two main signless Laplacian eigenvalues, and then ...
Deng, Hanyuan, Huang, He
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New bounds for the signless Laplacian spread [PDF]
, 2019 © 2018 Elsevier Inc.Let G be an undirected simple graph. The signless Laplacian spread of G is defined as the maximum distance of pairs of its signless Laplacian eigenvalues.
Leal, Laura +7 more
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