On the algebraic connectivity of token graphs
Web11 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 … 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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Web10 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 … 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
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 … 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 ...
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 … 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 …
Web30 de abr. 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 $F_k(G)$ …
WebThe properties of token graphs have been studied since 1991 by various authors and with different names, see, e.g., [1,2,3,5,9] and, in recent years, the study of its combinatorial properties and ... iop nhs meaningWeblinear 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 on the oregon trail written by: david hamlinWeb7 de jun. de 2024 · The algebraic connectivity of a graph is the second smallest eigenvalue of its Laplacian matrix. Algebraic connectivity is closely related to the traditional vertex (edge) connectivity and it plays an important role in the design of various networks. In this paper, we determine the graph which has the minimum algebraic … iop neuromorphicWebIn 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 connectivity (or … iop new yorkWebIn the mathematical field of knot theory, an algebraic link is a link that can be decomposed by Conway spheres into 2-tangles. Algebraic links are also called arborescent links . [2] … on the oregon trail robert vaughanWeb11 de mai. de 2024 · with the notion of graph connectivity. Recently Jord´ an and T anigawa [7] (building on Zhu a nd Hu [10, 11] who considered the 2-dimensional case) introdu ced the following quantita- iop new britain ctWebSince 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 ... on theoretical sociology