On the laplacian spread of graphs
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 …
On the laplacian spread of graphs
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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 ... Webbound for the spread of the line graph as function of the Zagreb index and the number of edges of the graph is obtained. In Section 3, relations among the spread of the line graph and the signless Laplacian spread are given. A su cient condition for the spread of a unicyclic graph with an odd girth to be at most the spread of its line graph is ...
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 … 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,
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 … WebOn the other hand, the Laplacian spread of a graph G, s L(G), is the di erence among the largest and the second smallest Laplacian eigenvalue of G. In [17] it was proven that …
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 …
Web4 de abr. de 2024 · April 2024; Authors: J. Nolan Faught nothing bundt cupcake caloriesWeb20 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 … how to set up dyno in discordWeb17 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 ]. nothing bundt lincoln neWebAbstract. 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 … how to set up dynabook docking stationWeb17 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. nothing bundt thankful free printableWeb15 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 … how to set up dynamic lockWeb10 de abr. de 2024 · Bao, Tan and Fan [Y.H. Bao, Y.Y. Tan,Y.Z. Fan, The Laplacian spread of unicyclic graphs, Appl. Math. Lett. 22 (2009) 1011–1015.] characterize the … nothing bundt promotional code