On the algebraic connectivity of token graphs
Web25 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 … 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 …
On the algebraic connectivity of token graphs
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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 ... 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.
WebPrototype-based Embedding Network for Scene Graph Generation Chaofan Zheng · Xinyu Lyu · Lianli Gao · Bo Dai · Jingkuan Song Efficient Mask Correction for Click-Based … 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 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 … 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...
Web13 de abr. de 2024 · The aim of this note is to revisit the connections between some stochastic games, namely Tug-of-War games, and a class of nonlocal PDEs on graphs. …
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 grace fanyiWeb15. 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 ... grace fancy nancyWebThis paper introduces token graphs and studies some of their properties including: connectivity, diameter, cliques, chromatic number, Hamiltonian paths, and Cartesian … chilled vs cooling waterWebwe 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. chilled vodka shotsWeb25 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 … chilled water ahu catalogueWeb1 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 ) … chilled warehouseWebthe 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]. chilled wallpapers