On the laplacian spread of graphs

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August undefined, 2024

WebIn this work, by combining old techniques of interlacing eigenvalues and rank $1$ perturbation matrices new lower bounds on the Laplacian spread of graphs are deduced, some of them involving invariant parameters of graphs, as it is the case of the bandwidth, independence number and vertex connectivity. Peer review: yes: URI: Web6 de fev. de 2024 · We establish sharp lower and upper bounds for the normalized signless Laplacian spreads of connected graphs. In addition, we present a better lower …

The Laplacian spread of graphs Request PDF - ResearchGate

Weboriented normal graph OG = (V,AG) results in the adjacency matrix AOG for oriented normal graphs of deﬁnition (1.10). Proof. As argued before, every oriented normal graph OG = … Web1 de abr. de 2024 · Download Citation On Apr 1, 2024, B.R. Rakshith and others published On distance Laplacian spectral determination of complete multipartite graphs Find, … sharon tong

Some results on the Laplacian spread of a graph

WebAbstract. In this paper we consider the energy of a simple graph with respect to its Laplacian eigenvalues, and prove some basic properties of this energy. In particular, we … 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), … Web17.1. 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, sharon tomski

Bounds for Di erent Spreads of Line and Total Graphs

WebRecently, the spread of a graph has received much attention. In [1], Petrovi¶c determined all minimal graphs whose spreads do not exceed 4. In [2] and [3], some lower and upper bounds for the spread of a graph were given. After then, the maximal spreads among all unicyclic graphs and all bicyclic graphs were determined in [4] and [5 ... Web11 de jan. de 2024 · Abstract: We conjecture a new lower bound on the algebraic connectivity of a graph that involves the number of vertices of high eccentricity in … porch cafe lightsWeb6 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 … sharon tompkins attorney

"Web15 de set. de 2016 · The Laplacian spread of a graph G with n vertices is defined to be s L (G) = μ 1 (G) − μ n − 1 (G), where μ 1 (G), μ n − 1 (G) are the largest and the second … " - On the laplacian spread of graphs

On the laplacian spread of graphs

On the Sum and Spread of Reciprocal Distance Laplacian …

Web1 de dez. de 2011 · The Laplacian spread s (G)s (G) of a graph GG is defined to be the difference between the largest eigenvalue and the second-smallest eigenvalue of the …

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Weblower bounds for the Laplacian spread of a connected graph that are related with the edge density. Then, using these results we study lower bounds for the Laplacian spread of graphs that have a particular nontrivial subset of vertices, namely for graphs that have an independent nontrivial subset of ver-tices and a (κ,τ)-regular subset of ... Web20 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 …

Web1 de dez. de 2015 · In what follows, based on Lemma 2.6, a few lower bounds on the Laplacian spread of a graph are obtained. Theorem 3.1. Let G be a graph of order n, … 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 …

Web1 de jan. de 2024 · The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of its … 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.

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 …

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 … porch cafe galveston happy hourWeb11 de jun. de 2024 · Article history: Received 9 June 2009 Accepted 27 August 2009 Available online 23 September 2009 Submitted by R.A. Brualdi AMS classification: 15A18 05C50 Keywords: Laplacian spread Unicyclic graphs Algebraic connectivity The Laplacian spread of a graph [1] is defined as the difference between the largest … sharon to natick maWebHodge 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 sharon toms realtor facebookWebLet 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. sharon toney finchWeb22 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 … sharon tomlinson shorewestWeb1 de jul. de 2013 · In this paper, we investigate Laplacian spread of graphs, and prove that there exist exactly five types of tricyclic graphs with maximum Laplacian spread among … sharon tongol molinaWeb4 de abr. de 2024 · April 2024; Authors: J. Nolan Faught sharon toms