2024 On the algebraic connectivity of token graphs

On the algebraic connectivity of token graphs

Author: ernx

August undefined, 2024

Web1 de mai. de 2024 · In this paper we show that such a lower bound remains true in the context of edge-connectivity. Specifically, we show that if G is t-edge-connected and \ … 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 …

Algebraic connectivity - Wikipedia

Web11 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- Webwe say that the connectivity of a graph is optimal. 3 Algebraic connectivity in random graph of Erdos-R˝ ´enyi In this section we give an analytical estimate of the algebraic connectivity in the Erdo˝s-Re´nyi random graph. The analytical estimate relies on the equality with the minimum nodal degree. citylink pick up call

The connected edge-maximal graphs on 5,. .. , 10 vertices whose 2-token …

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 … Web19 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 … 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 ... citylink prices list

Algebraic connectivity: local and global maximizer graphs IEEE ...

a arXiv:2209.01030v1 [math.CO] 2 Sep 2024 - ResearchGate

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 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 … citylink pricesWebThe algebraic connectivity of a graph is the numerically second smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of a graph . In other … citylink pricing

"Webdeﬁned the absolute algebraic connectivity of a graph as the maximum value of λ (L) over all nonnegative edge weights that add up to m, i.e., 1/m times the optimal value of (3). The problem of ﬁnding the absolute algebraic connectivity of a graph was discussed in [15, 16], and an analytical solution was presented for tree graphs. " - On the algebraic connectivity of token graphs

On the algebraic connectivity of token graphs

Algebraic connectivity of the second power of a graph

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 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 …

Did you know?

WebIn this video, we look at how to compute the algebraic connectivity of a graph, which is equivalent to the second-smallest eigenvalue of the simple Laplacian... 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 = …

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 … 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 …

WebPrototype-based Embedding Network for Scene Graph Generation Chaofan Zheng · Xinyu Lyu · Lianli Gao · Bo Dai · Jingkuan Song Efficient Mask Correction for Click-Based … WebThe algebraic connectivity of a graph is defined as the second smallest eigenvalue of the Laplacian matrix of the graph, which is a parameter to measure how well a graph is connected. In this paper, we present two unique graphs whose algebraic connectivity attain the minimum among all graphs whose complements are trees, but not stars, and …

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 ...

Web1 de jan. de 1973 · As other invariants reflecting the capability of graph connectivity, the algebraic connectivity is considered as a quantitative measurement of graph … city link promo codeWebthe 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]. citylink psychological servicesWebIn 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] … citylink propertiesWebThis paper introduces token graphs and studies some of their properties including: connectivity, diameter, cliques, chromatic number, Hamiltonian paths, and Cartesian … citylink promotional codesWebSince 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 ... citylink puchong branchWebThe 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 … citylink propertyWebThe 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 ... city link property management