On the algebraic connectivity of token graphs

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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 … 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 ) …

On the $d$-dimensional algebraic connectivity of graphs

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 ... 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 … ear pain with wax

Graph Analysis with Networkx and Python - Algebraic Connectivity ...

WebIn 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 … 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 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 … ear pain with scalp sensitivity

On the algebraic connectivity of token graphs - Semantic Scholar

Lower bounds of the Laplacian spectrum of graphs based on …

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 … 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 … ear palpitationsWebThe 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 ... ear pain with no sign of infection

"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 = … " - On the algebraic connectivity of token graphs

On the algebraic connectivity of token graphs

The Algebraic Connectivity of Graphs with Given Matching …

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 … 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 …

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WebPrototype-based Embedding Network for Scene Graph Generation Chaofan Zheng · Xinyu Lyu · Lianli Gao · Bo Dai · Jingkuan Song Efficient Mask Correction for Click-Based … 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-

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 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. 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].

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 … 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.

WebSince 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 ...

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 … ct4 v blackwing wikiWeb11 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. ct4v blackwing reviewsWebThe 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 … ear palpitations left earWebThe 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 … ear part 736.2 b 3 viWeb15 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 … ear pain with migraineWeb7 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 … ct4 v blackwing weightWebwe 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. ear pain word