On the laplacian spread of graphs

Author: lyjb

August undefined, 2024

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.

Upper bounds on the Laplacian spread of graphs

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 … 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 … incident meaning physics

A Nordhaus-Gaddum type problem for the normalized Laplacian …

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, Web1 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 … 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. incident management teams wildfire

Some results on the Laplacian spread of a graph

p-Laplacian Operators on Hypergraphs arXiv:2304.06468v1 …

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: Web13 de abr. de 2024 · In this Element, the authors consider fully discretized p-Laplacian problems (evolution, boundary value and variational problems) on graphs. The … incident objectives 202WebThe 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 for this graph invariant, that depends on rst Zagreb index, is given. Moreover, another upper bound is obtained and ex- inborn stimulus

"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 = … " - On the laplacian spread of graphs

On the laplacian spread of graphs

On the Laplacian spread of digraphs Request PDF - ResearchGate

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 … WebThis 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 …

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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, Web8 de ago. de 2024 · The Laplacian spread of a graph is the difference between the largest and second smallest Laplaicain eigenvalues of the graph. Using the Laplacian spread …

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 … Web17 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 ].

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, … 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 …

Web23 de nov. de 2024 · Abstract The spread of a graph is the difference between the largest and most negative eigenvalue of its adjacency matrix. We show that for sufficiently large …

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 … inborn rightsWebIn this article, we extend the notion of the Laplacian spread to simple directed graphs (digraphs) using the restricted numerical range. First, 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 … inborn predispositionWebFor 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. inborn responseWeb20 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 … incident metric servicenowWebtions 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 … inborn starWeblower 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 ... incident near missWebNew conjectures on algebraic connectivity and the Laplacian spread of graphs Wayne Barrett∗, Emily Evans †, H. Tracy Hall ‡, and Mark Kempton § Abstract We conjecture a … incident of 1773