On the algebraic connectivity of token graphs

Author: jrfo

August undefined, 2024

WebThe algebraic connectivity of a graph is the second smallest eigenvalue of the associated Laplacian matrix. In this paper, we not only characterize the extremal graphs with the … Web15 de jan. de 2007 · In Section 2, we also consider the diameter of G and give lower bounds of the Laplacian spectral radius and algebraic connectivity of G involving the diameter. 2. Lower bounds for the Laplacian eigenvalues Let G be a simple connected graph and L (G) = D (G) − A (G) be the Laplacian matrix of G. It is well known that λ n …

Minimizing Effective Resistance of a Graph - Stanford University

Web15 de set. de 2024 · For each of the following classes of graphs, the algebraic connectivity of a token graph F k (G) equals the algebraic connectivity of G. (i) Let G … Web5 de jun. de 2024 · For a graph G, let λ2(G) denote its second smallest Laplacian eigenvalue. It was conjectured that λ2(G)+λ2(G¯) ... A note on the algebraic … lakeland tag agency lakeland fl

The Algebraic Connectivity 10 Applications of Combinatorial …

Web2 de jan. de 2024 · Algebraic connectivity is one way to quantify graph connectivity, which in turn gauges robustness as a network. In this paper, we consider the problem of maximizing algebraic connectivity both locally and globally overall simple, undirected, unweighted graphs with a given number of vertices and edges. We pursue this … Web15 de out. de 2024 · The second smallest eigenvalue λ 2 ( G) is also called the algebraic connectivity of G and is an important indicator related to various properties of the … Web11 de mai. de 2024 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. lakeland teak patio set

Algebraic connectivity: local and global maximizer graphs

Regularity and Planarity of Token Graphs - Semantic Scholar

WebIn Section 5.3 we develop upper and lower bounds on the algebraic connectivity of graphs in terms of a graph’s diameter and mean distance. Since graphs with large diameter and mean distance tend to have less edges, they are “less connected” and thus have lower algebraic connectivity. Section 5.4 focuses on using the edge density of a ... Weblinear algebra were used to analyze adjacency matrices of graphs. Algebraic meth-ods have proven to be especially e ective in treating graphs which are regular and symmetric. Sometimes, certain eigenvalues have been referred to as the \algebraic connectivity" of a graph [127]. There is a large literature on algebraic aspects of jenga game big blocksWebthe algebraic connectivity of a graph. Throughout this paper, we consider connected graphs. The value of 2 encodes a great deal of information about G: its value is non-decreasing in the number of edges in G, and algebraic connectivity is closely related to graph diameter and various other algebraic properties of graphs [24]. jenga game online

"Web19 de jun. de 2024 · This paper introduces token graphs and studies some of their properties including: connectivity, diameter, cliques, chromatic number, Hamiltonian paths, and Cartesian products of token graphs. Expand 37 " - On the algebraic connectivity of token graphs

On the algebraic connectivity of token graphs

Lower bounds of the Laplacian spectrum of graphs based on …

Web13 de abr. de 2024 · The aim of this note is to revisit the connections between some stochastic games, namely Tug-of-War games, and a class of nonlocal PDEs on graphs. … Web1 de dez. de 2006 · We find an upper bound on the algebraic connectivity of graphs of various genus. We begin by showing that for fixed k ⩾ 1, the graph of genus k of largest …

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WebThe algebraic connectivity of a graph is one of the most well-studied parameters in spectral graph theory. It is de ned as the second smallest eigenvalue of the … WebPrototype-based Embedding Network for Scene Graph Generation Chaofan Zheng · Xinyu Lyu · Lianli Gao · Bo Dai · Jingkuan Song Efficient Mask Correction for Click-Based …

WebWe study the algebraic connectivity (or second Laplacian eigenvalue) of token graphs, also called symmetric powers of graphs. The k-token graph F k(G) of a graph Gis the … Web2 de set. de 2024 · In this paper, we prove the conjecture for new inﬁnite families of graphs, such as trees and graphs with maximum degree large enough. We study the algebraic …

WebDownload scientific diagram The graph G and its complement graph G of Example 2.4. from publication: On the algebraic connectivity of token graphs We study the algebraic connectivity (or ... WebThis paper introduces token graphs and studies some of their properties including: connectivity, diameter, cliques, chromatic number, Hamiltonian paths, and Cartesian …

Web2 de set. de 2024 · Abstract:We study the algebraic connectivity (or second Laplacian eigenvalue) of token graphs, also called symmetric powers of graphs. The $k$-token …

Webwith them. The ﬁrst major section of this paper is a survey of key results in Spectral Graph Theory. There are fascinating results involving the connectivity, spanning trees, and a … jenga game amazonWebThe algebraic connectivity of a graph is the numerically second smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of a graph . In other … lakeland takeawayWeb10 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 unique … lakeland taupoWeb25 de mar. de 2024 · The k -token graph F_k (G) of G is the graph whose vertices are the k -subsets of V ( G ), where two vertices are adjacent in F_k (G) whenever their symmetric difference is an edge of G. In 2024 Leaños and Trujillo-Negrete proved that if G is t -connected and t\ge k, then F_k (G) is at least k (t-k+1) -connected. jenga game amazon ukWebSince of the introduction of the absolute algebraic connectivity and its characterization for trees, the only one result found in the literature is due to Kirkland and Pati [50]. They present an upper bound on a(G)ˆ as a function of n and the vertex connectivity of G. See [50] for more details. 3. Algebraic connectivity of graphs obtained from ... jenga game how to playWeb1 de out. de 2015 · We study the algebraic connectivity (or second Laplacian eigenvalue) of token graphs, also called symmetric powers of graphs. The k -token graph F k ( G ) … jenga game online unblockedWeb11 de jan. de 2024 · New conjectures on algebraic connectivity and the Laplacian spread of graphs. Wayne Barrett, Emily Evans, H. Tracy Hall, Mark Kempton. We conjecture a new lower bound on the algebraic connectivity of a graph that involves the number of vertices of high eccentricity in a graph. We prove that this lower bound implies a strengthening of … jenga game online price