On the algebraic connectivity of token graphs
Web11 de mai. de 2024 · The -dimensional algebraic connectivity of a graph , introduced by Jordán and Tanigawa, is a quantitative measure of the -dimensional rigidity of that is … 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 …
On the algebraic connectivity of token graphs
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Web15. The most common measures of connectivity are edge-connectivity and vertex-connectivity. The vertex-connectivity, or just connectivity, of a graph is the minimum number of vertices you have to remove before you can even hope to disconnect the graph. A graph is called k -vertex-connected, or just k -connected, if its connectivity is at least ... Web1 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 ) …
Web25 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 … Web30 de jan. de 2024 · After installation, run from algebraic_connectivity_directed import *. There are 4 main functions: Function algebraic_connectivity_directed: algebraic_connectivity_directed (G) returns a, b, M where a is the algebraic connectivity of the digraph G. The graph G is a networkx DiGraph object. The definitions of a, b, M = …
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 … WebThe algebraic connectivity of a graph is the numerically second smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of a graph . In other …
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 …
Webthe 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]. how did mount etna affect people socialyWeb19 de jun. de 2024 · In 2012 Fabila-Monroy et al. reintroduced the concept of k-token graph as “a model in which k indistinguishable tokens move from vertex to vertex along the … how did mount mckinley get its nameWebThe algebraic connectivity (also known as Fiedler value or Fiedler eigenvalue after Miroslav Fiedler) of a graph G is the second-smallest eigenvalue (counting multiple … how did mount fuji eruptWebSince 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 ... how many singaporeans are obeseWebThe algebraic connectivity of a graph is the numerically second smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of a graph G. In other words, it is the second smallest root of the graph's Laplacian polynomial. This eigenvalue is greater than 0 iff G is a connected graph. The ratio of the Laplacian spectral radius to … how many singaporeans own 2 propertiesWeb19 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 how many singaporean to 1 work permitWebIn 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 ... how did mount pinatubo form