On the algebraic connectivity of token graphs

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August undefined, 2024

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 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 …

Algebraic Connectivity of Graphs Request PDF - ResearchGate

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 ... 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 … great roasted carrots

On the algebraic connectivity of token graphs - NASA/ADS

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. 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 … 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 = … great roasts for kids

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

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 … 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. great roasts insultsWeb5 de out. 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 maximising algebraic connectivity both local and globally over all simple, undirected, unweighted graphs with a given number of vertices and edges. We pursue this … great robbery app

"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... " - On the algebraic connectivity of token graphs

On the algebraic connectivity of token graphs

The Edge-Connectivity of Token Graphs SpringerLink

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 … 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 …

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Web7 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 … 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 …

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 ... 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 … 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 …

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 …

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 … great roasts for people that are being toxicWebThis paper introduces token graphs and studies some of their properties including: connectivity, diameter, cliques, chromatic number, Hamiltonian paths, and Cartesian … flora and fauna nature companyWeb2 de set. de 2024 · We study the algebraic connectivity (or second Laplacian eigenvalue) of token graphs, also called symmetric powers of graphs. The $k$-token graph $F_k … great roasts for robloxWeb15 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 … great roast beef recipesWeb25 de jul. de 2024 · Some Background. The algebraic connectivity of a graph G is defined as the second smallest Laplacian eigenvalue of the graph and is denoted by a ( G). It is known that a ( G) ≤ 1 if G is a tree and in particular, when the tree is a star then equality holds. Further, if G is a complete graph, then a ( G) = n where n is the number of … flora and fauna new zealandWeblinear 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 flora and fauna of amazon basinWeb19 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 great roasted vegetable recipes