Results 61 to 70 of about 63,846 (213)
Bounds for the signless Laplacian energy
Linear Algebra and its Applications, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abreu, Nair +4 more
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New bounds for the signless Laplacian spread [PDF]
Linear Algebra and its Applications, 2019 Let $G$ be a simple graph. The signless Laplacian spread of $G$ is defined as the maximum distance of pairs of its signless Laplacian eigenvalues. This paper establishes some new bounds, both lower and upper, for the signless Laplacian spread. Several of these bounds depend on invariant parameters of the graph.
Enide Andrade +3 more
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A Note on Some Bounds of the α‐Estrada Index of Graphs
Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020 Let G be a simple graph with n vertices. Let A~αG=αDG+1−αAG, where 0 ≤ α ≤ 1 and A(G) and D(G) denote the adjacency matrix and degree matrix of G, respectively. EEαG=∑i=1neλi is called the α‐Estrada index of G, where λ1, ⋯, λn denote the eigenvalues of A~αG. In this paper, the upper and lower bounds for EEα(G) are given.
Yang Yang +3 more
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Eigenvalue bounds for the signless laplacian
Publications de l'Institut Mathematique, 2007 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 presented in the context of a number of computer-generated conjectures.
Cvetkovic, Dragos +2 more
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Construction for the Sequences of Q‐Borderenergetic Graphs
Mathematical Problems in Engineering, Volume 2020, Issue 1, 2020., 2020 This research intends to construct a signless Laplacian spectrum of the complement of any k‐regular graph G with order n. Through application of the join of two arbitrary graphs, a new class of Q‐borderenergetic graphs is determined with proof. As indicated in the research, with a regular Q‐borderenergetic graph, sequences of regular Q‐borderenergetic ...
Bo Deng +4 more
wiley +1 more source
Central vertex join and central edge join of two graphs
AIMS Mathematics, 2020 The central graph $C(G)$ of a graph $G$ is obtained by sub dividing each edge of $G$ exactly once and joining all the nonadjacent vertices in $G$. In this paper, we compute the adjacency, Laplacian and signless Laplacian spectra of central graph of a ...
Jahfar T K, Chithra A V
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Eigenvalue Bounds for the Signless $p$-Laplacian
The Electronic Journal of Combinatorics, 2018 We consider the signless $p$-Laplacian $Q_p$ of a graph, a generalisation of the quadratic form of the signless Laplacian matrix (the case $p=2$). In analogy to Rayleigh's principle the minimum and maximum of $Q_p$ on the $p$-norm unit sphere are called its smallest and largest eigenvalues, respectively.
Borba, Elizandro Max, Schwerdtfeger, Uwe
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Aα‐Spectral Characterizations of Some Joins
Journal of Mathematics, Volume 2020, Issue 1, 2020., 2020 Let G be a graph with n vertices. For every real α ∈ [0,1], write Aα(G) for the matrix Aα(G) = αD(G) + (1 − α)A(G), where A(G) and D(G) denote the adjacency matrix and the degree matrix of G, respectively. The collection of eigenvalues of Aα(G) together with multiplicities are called the Aα‐spectrum of G.
Tingzeng Wu, Tian Zhou, Naihuan Jing
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On the construction of L-equienergetic graphs
AKCE International Journal of Graphs and Combinatorics, 2015 For a graph G with n vertices and m edges, and having Laplacian spectrum μ1,μ2,…,μn and signless Laplacian spectrum μ1+,μ2+,…,μn+, the Laplacian energy and signless Laplacian energy of G are respectively, defined as LE(G)=∑i=1n|μi−2mn| and LE+(G)=∑i=1n ...
S. Pirzada, Hilal A. Ganie
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Bounds on the α‐Distance Energy and α‐Distance Estrada Index of Graphs
Discrete Dynamics in Nature and Society, Volume 2020, Issue 1, 2020., 2020 Let G be a simple undirected connected graph, then Dα(G) = αTr(G) + (1 − α)D(G) is called the α‐distance matrix of G, where α ∈ [0,1], D(G) is the distance matrix of G, and Tr(G) is the vertex transmission diagonal matrix of G. In this paper, we study some bounds on the α‐distance energy and α‐distance Estrada index of G.
Yang Yang +3 more
wiley +1 more source