On the laplacian spread of graphs

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August undefined, 2024

WebThe Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In this paper, we show that the star is the unique tree with maximal Laplacian spread among all trees of given order, and the path is the unique one with minimal Laplacian spread … WebNew conjectures on algebraic connectivity and the Laplacian spread of graphs Wayne Barrett∗, Emily Evans †, H. Tracy Hall ‡, and Mark Kempton § Abstract We conjecture a …

On spectral spread of generalized distance matrix of a graph

WebThe power graph 풢(S) of a semigroup S is a simple undirected graph whose vertex set is S itself, and any two distinct vertices are adjacent if one of them is a power of the other. ... Zhai, J. Shu and Y. Hong, On the Laplacian spread of graphs, Appl. Math. Lett. 24 ... WebFor a simple connected graph G, let . D (G), T r (G), D L (G) and . D Q (G), respectively, are the distance matrix, the diagonal matrix of the vertex transmissions, distance Laplacian matrix and the distance signless Laplacian matrix. sick instagram shore stein papier

The Laplacian Spectrum of a Graph - SIAM Journal on Matrix …

Web8 de abr. de 2024 · While the answer is no, meaning you could find two distinct graphs/manifolds with the same Laplacian spectrum, you can still learn a lot about the topology of a graph from studying the decay of the eigenvalues. As importantly, people have looked at the eigenvectors of the Laplacian. Web6 de mar. de 2024 · Let G be a connected graph of order n. The signless Laplacian spread of G is defined as SQ (G)=q_1 (G)-q_n (G), where q_1 (G) and q_n (G) are the … Webtions on graphs and Laplacian spread. Section 6 presents a question on the maximal Laplacian spread of connected graphs with n vertices and the extremal graphs. And … the phoenixher

Upper bounds on the Laplacian spread of graphs

[PDF] A Nordhaus-Gaddum type problem for the normalized Laplacian …

WebLet G be a graph. The Laplacian matrix L ( G) = D ( G) − A ( G) is the difference of the diagonal matrix of vertex degrees and the 0-1 adjacency matrix. Various aspects of the spectrum of L ( G) are investigated. Particular attention is given to multiplicities of integer eigenvalues and to the effect on the spectrum of various modifications of G. Web20 de jul. de 2015 · Lek-Heng Lim. This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order generalization of the graph Laplacian. We will … sick in recliner coldWeb17.1. DIRECTED GRAPHS, UNDIRECTED GRAPHS, WEIGHTED GRAPHS 743 Proposition 17.1. Let G =(V,E) be any undirected graph with m vertices, n edges, and c connected com-ponents. For any orientation of G, if B is the in-cidence matrix of the oriented graph G, then c = dim(Ker(B>)), and B has rank m c. Furthermore, sick instagram captions

"WebThe Laplacian spread of a graph Gis de ned as the di erence between the largest and the second smallest eigenvalue of the Laplacian matrix of G. In this work, an upper bound … " - On the laplacian spread of graphs

On the laplacian spread of graphs

Laplacian Spread and Some Hamiltonian Properties of Graphs

Web机译：在本文中，我们研究了P-LAPLACIANS的特征值和图形的Dirichlet边界条件。我们通过标志条件表征了第一个特征（和二分钟图的最大特征功能）。通过P-Laplacian的第 … Web25 de mar. de 2012 · The Laplacian spread of a graph is defined as the difference between the largest and second smallest eigenvalues of the Laplacian matrix of the …

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Web22 de abr. de 2024 · The Aα A α -spread of a graph is defined as the difference between the largest eigenvalue and the smallest eigenvalue of the associated Aα A α -matrix. In this paper, some lower and upper bounds on Aα A α -spread are obtained, which extend the results of A A -spread and Q Q -spread. Moreover, the trees with the minimum and the … WebOn the Laplacian spread of digraphs - ScienceDirect Linear Algebra and its Applications Volume 664, 1 May 2024, Pages 126-146 On the Laplacian spread of digraphs☆ …

WebFirst, we provide Laplacian spread values for several families of digraphs. Then, we prove sharp upper bounds on the Laplacian spread for all polygonal and balanced digraphs. In particular, we show that the validity of the Laplacian spread bound for balanced digraphs is equivalent to the Laplacian spread conjecture for simple undirected graphs, WebThe notion of Laplacian spread is very signiﬁcant in characterizing the global structural property of graphs. Recently, Fan et al [4] have showed that, among all trees with nvertices, K 1;n 1 and P n are the unique trees with the maximal Laplacian spread and minimal Laplacian spread, respectively. Bao [1] et al

Web13 de abr. de 2024 · Understanding how things spread across networks is paramount to numerous endeavors including the study of epidemics, social contagions, cascading failures and blackouts, neuronal avalanches, and much more. 41,42 41. J. P. Gleeson, “ Binary-state dynamics on complex networks: Pair approximation and beyond,” Phys. Rev. X 3(2), … Web17 de nov. de 2024 · Abstract. The Laplacian spread of a graph is the difference between the largest and second smallest Laplaicain eigenvalues of the graph. Using the Laplacian spread of a graph, we in this note present sufficient conditions for some Hamiltonian properties of the graph.

Web16 de jan. de 2024 · This value is then used to calculate the squared difference between the top k Laplacian eigenvalue pairs of the two nearest neighbor graphs. The sum of these squared differences is taken as the Eigensimilarity, which can serve as a measure for the degree of isomorphism between two vector spaces, in this case, a pair of monolingual …

WebCorpus ID: 257921566; A Nordhaus-Gaddum type problem for the normalized Laplacian spectrum and graph Cheeger constant @inproceedings{Faught2024ANT, title={A Nordhaus-Gaddum type problem for the normalized Laplacian spectrum and graph Cheeger constant}, author={J. Nolan Faught and Mark Kempton and Adam Knudson}, … the phoenix home acoustical wave machineWebThis is an elementary introduction to the Hodge Laplacian on a graph, a higher-order generalization of the graph Laplacian. We will discuss basic properties including … the phoenix gym south bostonWebLet G be a connected non-bipartite graph on n vertices with domination number @c@?n+13. We present a lower bound for the least eigenvalue of the signless … the phoenix has risenWeb17 de set. de 2024 · The Laplacian spread of a graph G is defined as L S (G) = μ 1 (G) − μ n − 1 (G), where μ 1 (G) and μ n − 1 (G) are, respectively, the largest and second smallest Laplacian eigenvalues of G. More on L S ( G ) can be found in [ 16 , 17 , 18 ]. sick integrationspaceWeb20 de mar. de 2024 · We obtain a relationship between the Laplacian energy and the distance Laplacian energy for graphs with diameter 2. We obtain lower bounds for the … the phoenix has risen from the ashesWebDiscrete Mathematics and Theoretical Computer Science DMTCS vol. 10:1, 2008, 79–86 The Laplacian Spread of a Tree Yi-Zheng Fan 1,2†, Jing Xu, Yi Wang , Dong Liang1‡ 1Key Laboratory of Intelligent Computing & Signal Processing Ministry of Education of the People’s Republic of China, Anhui University, Hefei 230039, P. R. China sick instrumental beatsWebHodge Laplacians on Graphs\ast Lek-Heng Lim\dagger Abstract. This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order generalization of the graph Laplacian. We will discuss basic properties including coho-mology and Hodge theory. The main feature of our approach is simplicity, requiring only the phoenix holdings company ltd