On the laplacian spread of graphs

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August undefined, 2024

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. 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.

Upper bounds on the Laplacian spread of graphs

Web15 de nov. de 2024 · In this paper, we determine the graphs whose line graphs achieve the smallest and the largest Laplacian spread, respectively, among all connected graphs … 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 = … open fit app cost

Bounds for Di erent Spreads of Line and Total Graphs

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 ... Web11 de abr. de 2024 · To see the progress on this conjecture, we refer to Yang and You and the references therein.The rest of the paper is organized as follows. In Sect. 2, we obtain … 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 for this graph invariant, that depends on rst Zagreb index, is given. Moreover, another upper bound is obtained and ex- open fist theatre company

Laplacian spectra of power graphs of certain prime-power …

On the laplacian spread of graphs

On the Sum and Spread of Reciprocal Distance Laplacian …

WebIn 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 … 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 …

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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 … 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 …

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 … WebLet 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 …

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☆ … 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 …

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, … open fish sauce bottleWeb22 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 … open fit beachbodyWebDiscrete 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 openfit and beachbodyWebFirst, 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, iowa state bank sac city routing numberWebOn 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 … open fit app reviewsWeblower 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 ... iowa state bank sac city realtyWeb10 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 … iowa state bank sanborn ia routing number